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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">QR code</span></span>
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<p>A <b>QR code,</b> short for <b>quick-response code</b>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> is a type of two-dimensional <a href="Barcode#Matrix_(2D)_codes" title="Barcode">matrix barcode</a> invented in 1994 by <a href="Masahiro_Hara" title="Masahiro Hara">Masahiro Hara</a> of the <a href="Japan" title="Japan">Japanese</a> company <a href="Denso#DENSO_Wave" title="Denso">Denso Wave</a> for labelling automobile parts.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> It features black squares on a white background with <a href="Fiducial_markers" class="mw-redirect" title="Fiducial markers">fiducial markers</a>, readable by imaging devices like cameras, and processed using <a href="Reed%E2%80%93Solomon_error_correction" title="Reed–Solomon error correction">Reed–Solomon error correction</a> until the image can be appropriately interpreted. The required data is then extracted from patterns that are present in both the horizontal and the vertical components of the QR image.<sup id="cite_ref-autogenerated1_4-0" class="reference"><a href="#cite_note-autogenerated1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>
</p><p>Whereas a barcode is a machine-readable optical image that contains information specific to the labeled item, the QR code contains the data for a locator, an identifier, and web-tracking. To store data efficiently, QR codes use four standardized modes of encoding: <a href="Number" title="Number">numeric</a>, <a href="Alphanumericals" title="Alphanumericals">alphanumeric</a>, <a href="Byte_pair_encoding" class="mw-redirect" title="Byte pair encoding">byte</a> or <a href="Binary_number" title="Binary number">binary</a>, and <a href="Kanji" title="Kanji">kanji</a>.<sup id="cite_ref-QRCodefeatures_5-0" class="reference"><a href="#cite_note-QRCodefeatures-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>
Compared to standard <a href="Universal_Product_Code" title="Universal Product Code">UPC barcodes</a>, the QR labeling system was applied beyond the automobile industry because of faster reading of the optical image and greater data-storage capacity in applications such as product tracking, item identification, time tracking, document management, and general marketing.<sup id="cite_ref-autogenerated1_4-1" class="reference"><a href="#cite_note-autogenerated1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>
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<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>
<p>The QR code system was invented in 1994, at the <a href="Denso#DENSO_Wave" title="Denso">Denso Wave</a> automotive products company in Japan.<sup id="cite_ref-qrcode_Rakib_6-0" class="reference"><a href="#cite_note-qrcode_Rakib-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The initial alternating-square design presented by the team of researchers, headed by <a href="Masahiro_Hara" title="Masahiro Hara">Masahiro Hara</a>, was influenced by the black counters and the white counters played on a <a href="Go_equipment#Board" title="Go equipment">Go board</a>;<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> the pattern of the position detection markers was determined by finding the least-used sequence of alternating black-white areas on printed matter, which was found to be (1:1:3:1:1).<sup id="cite_ref-qrcode_history_10-0" class="reference"><a href="#cite_note-qrcode_history-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-qrcode_Rakib_6-1" class="reference"><a href="#cite_note-qrcode_Rakib-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The functional purpose of the QR code system was to facilitate keeping track of the types and numbers of automobile parts, by replacing individually-scanned bar-code labels on each box of auto parts with a single label that contained the data of each label. The quadrangular configuration of the QR code system consolidated the data of the various bar-code labels with <i><a href="Kanji" title="Kanji">kanji</a></i>, <i><a href="Kana" title="Kana">kana</a></i>, and alphanumeric codes printed onto a single label.<sup id="cite_ref-Handbook_of_Augmented_Reality_11-0" class="reference"><a href="#cite_note-Handbook_of_Augmented_Reality-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-qrcode_history_10-1" class="reference"><a href="#cite_note-qrcode_history-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-qrcode_Rakib_6-2" class="reference"><a href="#cite_note-qrcode_Rakib-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Adoption">Adoption</h2></div>
<p>During June 2011, 14 million American mobile users scanned a QR code or a barcode. Some 58% of those users scanned a QR or barcode from their homes, while 39% scanned from retail stores; 53% of the 14 million users were men between the ages of 18 and 34.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>
</p><p>In 2022, 89 million people in the <a href="United_States" title="United States">United States</a> scanned a QR code using their mobile devices, up by 26 percent compared to 2020. The majority of QR code users used them to make <a href="Payment" title="Payment">payments</a> or to access product and <a href="Menu" title="Menu">menu</a> information.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>
</p><p>In September 2020, a survey found that 18.8 percent of consumers in the United States and the <a href="United_Kingdom" title="United Kingdom">United Kingdom</a> strongly agreed that they had noticed an increase in QR code use since the then-active <a href="COVID-19" title="COVID-19">COVID-19</a>-related restrictions had begun several months prior.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>
</p><p>As of 2024, QR codes are used in a much broader context, including both commercial tracking applications and convenience-oriented applications aimed at mobile phone users (termed mobile tagging). QR codes may be used to display text to the user, to open a <a href="Web_page" title="Web page">webpage</a> on the user's device, to add a <a href="VCard" title="VCard">vCard</a> contact to the user's device, to open a <a href="Uniform_Resource_Identifier" title="Uniform Resource Identifier">Uniform Resource Identifier</a> (URI), to connect to a wireless network, or to compose an email or text message. There are a great many QR code generators available as software or as online tools that are either free or require a paid subscription.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> The QR code has become one of the most-used types of two-dimensional code.<sup id="cite_ref-About2DCode_16-0" class="reference"><a href="#cite_note-About2DCode-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Standards">Standards</h2></div>
<p>Several standards cover the encoding of data as QR codes:<sup id="cite_ref-qrstandard1_17-0" class="reference"><a href="#cite_note-qrstandard1-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>
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<ul><li>October 1997 – AIM (Association for Automatic Identification and Mobility) International<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li>
<li>January 1999 – <a href="Japanese_Industrial_Standards" title="Japanese Industrial Standards">JIS</a> X 0510</li>
<li>June 2000 – <a href="International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a>/<a href="International_Electrotechnical_Commission" title="International Electrotechnical Commission">IEC</a> 18004:2000 <i>Information technology – Automatic identification and data capture techniques – Bar code symbology – QR code</i> (now withdrawn)<br> Defines QR code models 1 and 2 symbols.</li>
<li>1 September 2006 – ISO/IEC 18004:2006 <i>Information technology – Automatic identification and data capture techniques – QR Code 2005 bar code symbology specification</i> (now withdrawn)<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><br> Defines QR code 2005 symbols, an extension of QR code model 2. Does not specify how to read QR code model 1 symbols, or require this for compliance.</li>
<li>1 February 2015 – ISO/IEC 18004:2015 <i>Information – Automatic identification and data capture techniques – QR Code barcode symbology specification</i> (now withdrawn)<br> Renames the QR Code 2005 symbol to QR Code and adds clarification to some procedures and minor corrections. It was withdrawn and updated to 18004:2024 in August 2024, which optimizes encoding efficiency, improves error correction, and refines structured append functionality.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></li>
<li>May 2022 – ISO/IEC 23941:2022 <i>Information technology – Automatic identification and data capture techniques – Rectangular Micro QR Code (rMQR) bar code symbology specification</i><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><br>Defines the requirements for Micro QR Code.</li>
<li>August 2024 – ISO/IEC 18004:2024 Information technology — Automatic identification and data capture techniques — QR code bar code symbology specification</li></ul>
<p>At the <a href="Application_layer" title="Application layer">application layer</a>, there is some variation between most of the implementations. Japan's <a href="NTT_DoCoMo" class="mw-redirect" title="NTT DoCoMo">NTT DoCoMo</a> has established <a href="De_facto" title="De facto">de facto</a> standards for the encoding of URLs, contact information, and several other data types.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> The open-source "<a href="ZXing" class="mw-redirect" title="ZXing">ZXing</a>" project maintains a list of QR code data types.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Uses">Uses</h2></div>
<p>QR codes have become common in consumer advertising. Typically, a <a href="Smartphone" title="Smartphone">smartphone</a> is used as a QR code scanner, displaying the code and converting it to some useful form (such as a standard <a href="URL" title="URL">URL</a> for a website, thereby obviating the need for a user to type it into a <a href="Web_browser" title="Web browser">Web browser</a>).
</p><p>QR codes have become a focus of advertising strategy to provide a way to access a brand's website more quickly than by manually entering a URL.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Beyond mere convenience to the consumer, the importance of this capability is the belief that it increases the <a href="Conversion_rate" class="mw-redirect" title="Conversion rate">conversion rate</a>: the chance that contact with the advertisement will convert to a sale. It coaxes interested prospects further down the <a href="Conversion_funnel" title="Conversion funnel">conversion funnel</a> with little delay or effort, bringing the viewer to the advertiser's website immediately, whereas a longer and more targeted sales pitch may lose the viewer's interest.
</p><p>Although initially used to track parts in vehicle manufacturing, QR codes are used over a much wider range of applications. These include commercial tracking, warehouse stock control, entertainment and transport ticketing, product and loyalty marketing, and in-store product labeling. Examples of marketing include where a company's discounted and percent discount can be captured using a QR code decoder that is a mobile app, or storing a company's information such as address and related information alongside its alpha-numeric text data as can be seen in telephone directory <a href="Yellow_pages" title="Yellow pages">yellow pages</a>.
</p>
<p>They can also be used to store personal information for organizations. An example of this is the <a href="Philippines" title="Philippines">Philippines</a> <a href="National_Bureau_of_Investigation_(Philippines)" title="National Bureau of Investigation (Philippines)">National Bureau of Investigation</a> (NBI) where NBI clearances now come with a QR code. Many of these applications target <a href="Mobile_phone" title="Mobile phone">mobile-phone</a> users (via <a href="Mobile_tagging" title="Mobile tagging">mobile tagging</a>). Users may receive text, add a vCard contact to their device, open a URL, or compose an <a href="Email#Message_format" title="Email">e-mail</a> or text message after scanning QR codes. They can generate and print their own QR codes for others to scan and use by visiting one of several pay or free QR code-generating sites or apps. <a href="Google" title="Google">Google</a> had an <a href="API" title="API">API</a>, now deprecated, to generate QR codes,<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> and apps for scanning QR codes can be found on nearly all smartphone devices.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup>
</p>
<p>QR codes storing addresses and URLs may appear in magazines, on signs, on buses, on business cards, or on almost any object about which users might want information. Users with a <a href="Camera_phone" title="Camera phone">camera phone</a> equipped with the correct reader application can scan the image of the QR code to display text and contact information, connect to a <a href="Wireless_LAN" title="Wireless LAN">wireless network</a>, or open a web page in the phone's browser. This act of linking from physical world objects is termed <a href="Hardlink_(hyperlink)" class="mw-redirect" title="Hardlink (hyperlink)">hardlinking</a> or <a href="Object_hyperlinking" title="Object hyperlinking">object hyperlinking</a>. QR codes also may be linked to a location to track where a code has been scanned. Either the application that scans the QR code retrieves the geo information by using GPS and cell tower triangulation (aGPS) or the URL encoded in the QR code itself is associated with a location. In 2008, a Japanese stonemason announced plans to engrave QR codes on gravestones, allowing visitors to view information about the deceased, and family members to keep track of visits.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Psychologist <a href="Richard_Wiseman" title="Richard Wiseman">Richard Wiseman</a> was one of the first authors to include QR codes in a book, in <i><a href="Paranormality%3A_Why_We_See_What_Isn't_There" class="mw-redirect" title="Paranormality: Why We See What Isn't There">Paranormality: Why We See What Isn't There</a></i> (2011).<sup id="cite_ref-Skepicality160_30-0" class="reference"><a href="#cite_note-Skepicality160-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> <a href="Microsoft_Office" title="Microsoft Office">Microsoft Office</a> and <a href="LibreOffice" title="LibreOffice">LibreOffice</a> have a functionality to insert QR code into documents.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup>
</p><p>QR codes have been incorporated into currency. In June 2011, The <a href="Royal_Dutch_Mint" title="Royal Dutch Mint">Royal Dutch Mint</a> (<i>Koninklijke Nederlandse Munt</i>) issued the world's first official coin with a QR code to celebrate the centenary of its current building and premises. The coin can be scanned by a smartphone and originally linked to a special website with content about the historical event and design of the coin.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> In 2014, the Central Bank of Nigeria issued a 100-naira banknote to commemorate its centennial, the first banknote to incorporate a QR code in its design. When scanned with an internet-enabled mobile device, the code goes to a website that tells the centenary story of Nigeria.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup>
</p><p>In 2015, the <a href="Central_Bank_of_Russia" title="Central Bank of Russia">Central Bank of the Russian Federation</a> issued a 100-<a href="Ruble" title="Ruble">rubles</a> note to commemorate the <a href="Annexation_of_Crimea_by_the_Russian_Federation" class="mw-redirect" title="Annexation of Crimea by the Russian Federation">annexation of Crimea by the Russian Federation</a>.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> It contains a QR code into its design, and when scanned with an internet-enabled mobile device, the code goes to a website that details the historical and technical background of the commemorative note. In 2017, the <a href="Bank_of_Ghana" title="Bank of Ghana">Bank of Ghana</a> issued a 5-<a href="Ghanaian_cedi" title="Ghanaian cedi">cedis</a> banknote to commemorate 60 years of <a href="Central_bank" title="Central bank">central banking</a> in <a href="Ghana" title="Ghana">Ghana</a>. It contains a QR code in its design which, when scanned with an internet-enabled mobile device, goes to the official Bank of Ghana website.
</p><p>Credit card functionality is under development. In September 2016, the <a href="Reserve_Bank_of_India" title="Reserve Bank of India">Reserve Bank of India</a> (RBI) launched the eponymously named <a href="BharatQR" title="BharatQR">BharatQR</a>, a common QR code jointly developed by all the four major card payment companies – <a href="National_Payments_Corporation_of_India" title="National Payments Corporation of India">National Payments Corporation of India</a> that runs <a href="RuPay" title="RuPay">RuPay</a> cards along with <a href="Mastercard" title="Mastercard">Mastercard</a>, <a href="Visa_Inc." title="Visa Inc.">Visa</a>, and <a href="American_Express" title="American Express">American Express</a>. It will also have the capability of accepting payments on the <a href="Unified_Payments_Interface" title="Unified Payments Interface">Unified Payments Interface</a> (UPI) platform.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Augmented_reality">Augmented reality</h3></div>
<p>QR codes are used in some <a href="Augmented_reality" title="Augmented reality">augmented reality</a> systems to determine the positions of objects in 3-dimensional space.<sup id="cite_ref-Handbook_of_Augmented_Reality_11-1" class="reference"><a href="#cite_note-Handbook_of_Augmented_Reality-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Mobile_operating_systems">Mobile operating systems</h3></div>
<p>QR codes can be used on various mobile device operating systems. While initially requiring the installation and use of third-party apps, both Android and iOS (since iOS 11<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup>) devices can now natively scan QR codes, without requiring an external app to be used.<sup id="cite_ref-androidnative_40-0" class="reference"><a href="#cite_note-androidnative-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> The camera app can scan and display the kind of QR code along with the link. These devices support <a href="URL_redirection" title="URL redirection">URL redirection</a>, which allows QR codes to send <a href="Metadata" title="Metadata">metadata</a> to existing applications on the device.
</p>
<div class="mw-heading mw-heading3"><h3 id="Virtual_stores">Virtual stores</h3></div>
<p>QR codes have been used to establish "virtual stores", where a gallery of product information and QR codes is presented to the customer, e.g. on a train station wall. The customers scan the QR codes, and the products are delivered to their homes. This use started in <a href="South_Korea" title="South Korea">South Korea</a>,<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> and Argentina,<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> but is currently expanding globally.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> Walmart, Procter & Gamble and Woolworths have already adopted the Virtual Store concept.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="QR_code_payment">QR code payment</h3></div>
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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="QR_code_payment" title="QR code payment">QR code payment</a></div>
<p>QR codes can be used to store bank account information or credit card information, or they can be specifically designed to work with particular payment provider applications. There are several trial applications of QR code payments across the world.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> In developing countries including China,<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> India<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> QR code payment is a very popular and convenient method of making payments. Since <a href="Alipay" title="Alipay">Alipay</a> designed a QR code payment method in 2011,<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> mobile payment has been quickly adopted in China. As of 2018, around 83% of all payments were made via mobile payment.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup>
</p><p>In November 2012, QR code payments were deployed on a larger scale in the <a href="Czech_Republic" title="Czech Republic">Czech Republic</a> when an open format for payment information exchange – a <a href="Short_Payment_Descriptor" title="Short Payment Descriptor">Short Payment Descriptor</a> – was introduced and endorsed by the Czech Banking Association as the official local solution for QR payments.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> In 2013, the <a href="European_Payments_Council" class="mw-redirect" title="European Payments Council">European Payment Council</a> provided guidelines for the <a href="EPC_QR_code" title="EPC QR code">EPC QR code</a> enabling <a href="Giro_(banking)" title="Giro (banking)">SCT</a> initiation within the <a href="Eurozone" title="Eurozone">Eurozone</a>.
</p><p>In 2017, <a href="Singapore" title="Singapore">Singapore</a> created a task force including government agencies such as the <a href="Monetary_Authority_of_Singapore" title="Monetary Authority of Singapore">Monetary Authority of Singapore</a> and <a href="Infocomm_Media_Development_Authority" title="Infocomm Media Development Authority">Infocomm Media Development Authority</a> to spearhead a system for e-payments using standardized QR code specifications. These specific dimensions are specialized for Singapore.<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup>
</p><p>The e-payment system, Singapore Quick Response Code (SGQR), essentially merges various QR codes into one label that can be used by both parties in the payment system. This allows for various banking apps to facilitate payments between multiple customers and a merchant that displays a single QR code. The SGQR scheme is co-owned by MAS and IMDA.<sup id="cite_ref-sgqr_55-0" class="reference"><a href="#cite_note-sgqr-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> A single SGQR label contains e-payments and combines multiple payment options. People making purchases can scan the code and see which payment options the merchant accepts.<sup id="cite_ref-sgqr_55-1" class="reference"><a href="#cite_note-sgqr-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Website_login">Website login</h3></div>
<p>QR codes can be used to log into websites: a QR code is shown on the login page on a <a href="Computer_monitor" title="Computer monitor">computer screen</a>, and when a registered user scans it with a verified smartphone, they will automatically be logged in. Authentication is performed by the smartphone, which contacts the server. Google deployed such a login scheme in 2012.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Mobile_ticket">Mobile ticket</h3></div>
<p>There is a system whereby a QR code can be displayed on a device such as a smartphone and used as an <a href="Ticket_(admission)" title="Ticket (admission)">admission ticket</a>.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> Its use is common for <a href="J1_League" title="J1 League">J1 League</a> and <a href="Nippon_Professional_Baseball" title="Nippon Professional Baseball">Nippon Professional Baseball</a> tickets in Japan.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> In some cases, rights can be transferred via the Internet. In <a href="Latvia" title="Latvia">Latvia</a>, QR codes can be scanned in <a href="Riga" title="Riga">Riga</a> public transport to validate <a href="R%C4%ABgas_Satiksme" title="Rīgas Satiksme">Rīgas Satiksme</a> e-tickets.<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Restaurant_ordering">Restaurant ordering</h3></div>
<p>Restaurants can present a QR code near the front door or at the table allowing guests to view an online menu, or even redirect them to an online ordering website or app, allowing them to order or possibly pay for their meal without having to use a cashier or waiter. QR codes can also link to daily or weekly specials that are not printed on the standardized menus,<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> and enable the establishment to update the entire menu without needing to print copies. At table-serve restaurants, QR codes enable guests to order and pay for their meals without a waiter involved – the QR code contains the table number so servers know where to bring the food.<sup id="cite_ref-Verge,_Kastrenakes,_9/29/20_63-0" class="reference"><a href="#cite_note-Verge,_Kastrenakes,_9/29/20-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> This application has grown especially since the need for social distancing during the <a href="COVID-19_pandemic" title="COVID-19 pandemic">2020 COVID-19 pandemic</a> prompted reduced contact between service staff and customers.<sup id="cite_ref-Verge,_Kastrenakes,_9/29/20_63-1" class="reference"><a href="#cite_note-Verge,_Kastrenakes,_9/29/20-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Joining_a_Wi‑Fi_network">Joining a Wi‑Fi network</h3></div>
<p>By specifying the SSID, encryption type, password/passphrase, and if the SSID is hidden or not, mobile device users can quickly scan and join networks without having to manually enter the data.<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> A <a href="MeCard_(QR_code)" title="MeCard (QR code)">MeCard</a>-like format is supported by Android and iOS 11+.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup>
</p>
<ul><li>Common format: <code>WIFI:S:<SSID>;T:<WEP|WPA|nopass>;P:<PASSWORD>;H:<true|false|blank>;;</code></li>
<li>Sample: <code>WIFI:S:MySSID;T:WPA;P:MyPassW0rd;;</code></li></ul>
<div class="mw-heading mw-heading3"><h3 id="Funerary_use">Funerary use</h3></div>
<p>A QR code can link to an <a href="Obituary" title="Obituary">obituary</a> and can be placed on a <a href="Headstone" class="mw-redirect" title="Headstone">headstone</a>. In 2008, Ishinokoe in Yamanashi Prefecture, Japan began to sell tombstones with QR codes produced by IT DeSign, where the code leads to a virtual grave site of the deceased.<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> Other companies, such as Wisconsin-based Interactive Headstones, have also begun implementing QR codes into tombstones.<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> In 2014, the <a href="Jewish_Cemetery_of_La_Paz" class="mw-redirect" title="Jewish Cemetery of La Paz">Jewish Cemetery of La Paz</a> in Uruguay began implementing QR codes for tombstones.<sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Electronic_authentication">Electronic authentication</h3></div>
<p>QR codes can be used to generate <a href="Time-based_one-time_password" title="Time-based one-time password">time-based one-time passwords</a> for <a href="Electronic_authentication" title="Electronic authentication">electronic authentication</a>.
</p>
<div class="mw-heading mw-heading3"><h3 id="Loyalty_programs">Loyalty programs</h3></div>
<p>QR codes have been used by various retail outlets that have <a href="Loyalty_program" title="Loyalty program">loyalty programs</a>. Sometimes these programs are accessed with an <a href="Mobile_app" title="Mobile app">app</a> that is loaded onto a phone and includes a process triggered by a QR code scan. The QR codes for loyalty programs tend to be found printed on the <a href="Receipt" title="Receipt">receipt</a> for a purchase or on the products themselves. Users in these schemes collect award points by scanning a code.
</p>
<div class="mw-heading mw-heading3"><h3 id="Counterfeit_detection">Counterfeit detection</h3></div>
<p>Serialised QR codes have been used by brands<sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> and governments<sup id="cite_ref-72" class="reference"><a href="#cite_note-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> to let consumers, retailers and distributors verify the authenticity of the products and help with detecting counterfeit products, as part of a <a href="Brand_protection" title="Brand protection">brand protection</a> program.<sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> However, the security level of a regular QR code is limited since QR codes printed on original products are easily reproduced on fake products, even though the analysis of data generated as a result of QR code scanning can be used to detect counterfeiting and illicit activity.<sup id="cite_ref-74" class="reference"><a href="#cite_note-74"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> A higher security level can be attained by embedding a <a href="Digital_watermark" class="mw-redirect" title="Digital watermark">digital watermark</a> or <a href="Copy_detection_pattern" title="Copy detection pattern">copy detection pattern</a> into the image of the QR code. This makes the QR code more secure against counterfeiting attempts; products that display a code which is counterfeit, although valid as a QR code, can be detected by scanning the secure QR code with the appropriate app.<sup id="cite_ref-75" class="reference"><a href="#cite_note-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup>
</p><p>The treaty regulating <a href="Apostille" class="mw-redirect" title="Apostille">apostilles</a> (documents bearing a seal of authenticity), has been updated to allow the issuance of digital apostilles by countries; a digital apostille is a PDF document with a <a href="Cryptographic_signature" class="mw-redirect" title="Cryptographic signature">cryptographic signature</a> containing a QR code for a canonical URL of the original document, allowing users to verify the apostille from a printed version of the document.
</p>
<div class="mw-heading mw-heading3"><h3 id="Product_tracing">Product tracing</h3></div>
<div role="note" class="hatnote navigation-not-searchable">Further information: <a href="Produce_traceability" title="Produce traceability">Produce traceability</a></div>
<p>Different studies have been conducted to assess the effectiveness of QR codes as a means of conveying labelling information and their use as part of a food traceability system. In a field experiment, it was found that when provided free access to a smartphone with a QR code scanning app, 52.6% of participants would use it to access labelling information.<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup> A study made in South Korea showed that consumers appreciate QR code used in food traceability system, as they provide detailed information about food, as well as information that helps them in their purchasing decision.<sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup> If QR codes are serialised, consumers can access a web page showing the supply chain for each ingredient, as well as information specific to each related batch, including meat processors and manufacturers, which helps address the concerns they have about the origin of their food.<sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="COVID-19_pandemic">COVID-19 pandemic</h3></div>
<p>After the <a href="COVID-19_pandemic" title="COVID-19 pandemic">COVID-19 pandemic</a> began spreading, QR codes began to be used as a "touchless" system to display information, show menus, or provide updated consumer information, especially in the hospitality industry. Restaurants replaced paper or laminated plastic menus with QR code decals on the table, which opened an online version of the menu. This prevented the need to dispose of single-use paper menus, or institute cleaning and sanitizing procedures for permanent menus after each use.<sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup> Local television stations have also begun to utilize codes on <a href="Local_news" title="Local news">local newscasts</a> to allow viewers quicker access to stories or information involving the pandemic, including testing and immunization scheduling websites, or for links within stories mentioned in the newscasts overall.
</p><p>In <a href="Australia" title="Australia">Australia</a>, patrons were required to scan QR codes at shops, clubs, supermarkets, and other service and retail establishments on entry to assist <a href="Contact_tracing" title="Contact tracing">contact tracing</a>. Singapore, <a href="Taiwan" title="Taiwan">Taiwan</a>, the United Kingdom, and <a href="New_Zealand" title="New Zealand">New Zealand</a> used similar systems.<sup id="cite_ref-abc-qr-code-tracing_80-0" class="reference"><a href="#cite_note-abc-qr-code-tracing-80"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup>
</p><p>QR codes are also present on COVID-19 vaccination certificates in places such as <a href="Canada" title="Canada">Canada</a> and the <a href="European_Union" title="European Union">EU</a> (<a href="EU_Digital_COVID_Certificate" title="EU Digital COVID Certificate">EU Digital COVID certificate</a>), where they can be scanned to verify the information on the certificate.<sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Design">Design</h2></div>
<p>Unlike the older, one-dimensional barcodes that were designed to be mechanically scanned by a narrow beam of light, a QR code is detected by a two-dimensional digital <a href="Image_sensor" title="Image sensor">image sensor</a> and then digitally analyzed by a programmed processor. The processor locates the three finder patterns, each consisting of three superimposed concentric squares of differing contrast at the upper left, upper right and lower left corners of the QR code image,<sup id="cite_ref-82" class="reference"><a href="#cite_note-82"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup> using a smaller square (or multiple squares) near the fourth corner to normalize the image for size, orientation, and angle of viewing. The small dots throughout the QR code are then converted to binary numbers and validated with an error-correcting algorithm.
</p>
<div class="mw-heading mw-heading3"><h3 id="Information_capacity">Information capacity</h3></div>
<p>The amount of data that can be represented by a QR code symbol depends on the data type (<i>mode</i>, or input character set), version (1, ..., 40, indicating the overall dimensions of the symbol, i.e. 4 × version number + 17 dots on each side), and <a href="#Error_correction">error correction</a> level. The maximum storage capacities occur for version 40 and error correction level L (low), denoted by 40-L:<sup id="cite_ref-About2DCode_16-1" class="reference"><a href="#cite_note-About2DCode-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-83" class="reference"><a href="#cite_note-83"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup>
</p>
<table class="wikitable">
<caption>Maximum character storage capacity (40-L) <br><small><i>Character</i> refers to individual values of the input mode (data type).</small>
</caption>
<tbody><tr>
<th>Input mode
</th>
<th>Max. characters</th>
<th>Bits/char.</th>
<th>Possible characters, default encoding
</th></tr>
<tr>
<th>Numeric only
</th>
<td>7,089</td>
<td>3<style data-mw-deduplicate="TemplateStyles:r1154941027">
/* start https://en.wikipedia.org/ */
.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}
/* end https://en.wikipedia.org/ */
</style><span class="frac"><span class="num">1</span>⁄<span class="den">3</span></span></td>
<td>0, 1, 2, 3, 4, 5, 6, 7, 8, 9
</td></tr>
<tr>
<th><a href="Alphanumeric" class="mw-redirect" title="Alphanumeric">Alphanumeric</a>
</th>
<td>4,296</td>
<td>5<span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span></td>
<td>0–9, A–Z (upper-case only), space, $, %, *, +, -, ., /, :
</td></tr>
<tr>
<th><a href="Binary_numeral_system" class="mw-redirect" title="Binary numeral system">Binary</a>/byte
</th>
<td>2,953</td>
<td>8</td>
<td><a href="ISO/IEC_8859-1" title="ISO/IEC 8859-1">ISO/IEC 8859-1</a>
</td></tr>
<tr>
<th><a href="Kanji" title="Kanji">Kanji</a>/<a href="Kana" title="Kana">kana</a>
</th>
<td>1,817</td>
<td>13</td>
<td><a href="Shift_JIS" title="Shift JIS">Shift JIS</a> <a href="JIS_X_0208" title="JIS X 0208">X 0208</a>
</td></tr></tbody></table>
<p>Here are some samples of QR codes:
</p>
<ul class="gallery mw-gallery-traditional">
<li class="gallerybox" style="width: 255px">
<div class="thumb" style="width: 250px; height: 250px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Version 1 (21×21). Content: "Ver1"</div>
</li>
<li class="gallerybox" style="width: 255px">
<div class="thumb" style="width: 250px; height: 250px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Version 2 (25×25). Content: "Version 2"</div>
</li>
<li class="gallerybox" style="width: 255px">
<div class="thumb" style="width: 250px; height: 250px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Version 3 (29×29). Content: "Version 3 QR Code"</div>
</li>
<li class="gallerybox" style="width: 255px">
<div class="thumb" style="width: 250px; height: 250px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Version 4 (33×33). Content: "Version 4 QR Code, up to 50 char"</div>
</li>
<li class="gallerybox" style="width: 255px">
<div class="thumb" style="width: 250px; height: 250px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Version 10 (57×57). Content: "VERSION 10 QR CODE, UP TO 174 CHAR AT H LEVEL, WITH 57X57 MODULES AND PLENTY OF ERROR CORRECTION TO GO AROUND. NOTE THAT THERE ARE ADDITIONAL TRACKING BOXES" (actually encoded in all capital letters). (Tracking boxes are more commonly called <i>alignment patterns</i>.)</div>
</li>
<li class="gallerybox" style="width: 255px">
<div class="thumb" style="width: 250px; height: 250px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Version 25 (117×117). Content: 1,269 characters of ASCII text describing QR codes</div>
</li>
<li class="gallerybox" style="width: 255px">
<div class="thumb" style="width: 250px; height: 250px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Version 40 (177×177). Content: "Version 40 QR Code can contain up to 1852 chars ..." (and followed by four paragraphs of ASCII text describing QR codes). The text refers to a QR Code with a "Level H" error correction. Other levels provide higher capacity.</div>
</li>
</ul>
<div class="mw-heading mw-heading3"><h3 id="Error_correction">Error correction</h3></div>
<p>QR codes use <a href="Reed%E2%80%93Solomon_error_correction" title="Reed–Solomon error correction">Reed–Solomon error correction</a> over the <a href="Finite_field" title="Finite field">finite field</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {F} _{256}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">F</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>256</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mathbb {F} _{256}}</annotation>
</semantics>
</math></span><img src="./3aae762a2df30726681155bd3c3fc1c2036011f9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.118ex; height:2.509ex;" alt="{\displaystyle \mathbb {F} _{256}}" loading="lazy"></span> or <span class="texhtml">GF(2<sup>8</sup>)</span>, the elements of which are encoded as <a href="Octet_(computing)" title="Octet (computing)">bytes of 8 bits</a>; the byte <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b_{7}b_{6}b_{5}b_{4}b_{3}b_{2}b_{1}b_{0}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>7</mn>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>6</mn>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>5</mn>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b_{7}b_{6}b_{5}b_{4}b_{3}b_{2}b_{1}b_{0}}</annotation>
</semantics>
</math></span><img src="./137ef5fd0ae4fd285e6f0e4db882f616fd2bc31a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.414ex; height:2.509ex;" alt="{\displaystyle b_{7}b_{6}b_{5}b_{4}b_{3}b_{2}b_{1}b_{0}}" loading="lazy"></span> with a standard numerical value <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle \sum _{i=0}^{7}b_{i}2^{i}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mstyle displaystyle="false" scriptlevel="0">
<munderover>
<mo>∑<!-- ∑ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>7</mn>
</mrow>
</munderover>
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
<msup>
<mn>2</mn>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msup>
</mstyle>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \textstyle \sum _{i=0}^{7}b_{i}2^{i}}</annotation>
</semantics>
</math></span><img src="./55629aba21ee4a09f43702d43694991ef2d2e12f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.5ex; height:3.509ex;" alt="{\displaystyle \textstyle \sum _{i=0}^{7}b_{i}2^{i}}" loading="lazy"></span> encodes the field element <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle \sum _{i=0}^{7}b_{i}\alpha ^{i}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mstyle displaystyle="false" scriptlevel="0">
<munderover>
<mo>∑<!-- ∑ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>7</mn>
</mrow>
</munderover>
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msup>
</mstyle>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \textstyle \sum _{i=0}^{7}b_{i}\alpha ^{i}}</annotation>
</semantics>
</math></span><img src="./756047107c1ba315990894c577708ad1f1870a17.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.826ex; height:3.509ex;" alt="{\displaystyle \textstyle \sum _{i=0}^{7}b_{i}\alpha ^{i}}" loading="lazy"></span> where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha \in \mathbb {F} _{256}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>α<!-- α --></mi>
<mo>∈<!-- ∈ --></mo>
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">F</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>256</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha \in \mathbb {F} _{256}}</annotation>
</semantics>
</math></span><img src="./bd800ad6bd2fea8492aee17c266dee4bd26f6ec5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.447ex; height:2.509ex;" alt="{\displaystyle \alpha \in \mathbb {F} _{256}}" loading="lazy"></span> is taken to be a primitive element satisfying <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ^{8}+\alpha ^{4}+\alpha ^{3}+\alpha ^{2}+1=0}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>8</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>1</mn>
<mo>=</mo>
<mn>0</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha ^{8}+\alpha ^{4}+\alpha ^{3}+\alpha ^{2}+1=0}</annotation>
</semantics>
</math></span><img src="./4ab9c98c72dc6466551973982f0a62b81644955c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:26.952ex; height:2.843ex;" alt="{\displaystyle \alpha ^{8}+\alpha ^{4}+\alpha ^{3}+\alpha ^{2}+1=0}" loading="lazy"></span>. The primitive polynomial is <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{8}+x^{4}+x^{3}+x^{2}+1}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>8</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>1</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle x^{8}+x^{4}+x^{3}+x^{2}+1}</annotation>
</semantics>
</math></span><img src="./cc93fb90271cad55cd6526d07e706a61c06cb061.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:22.06ex; height:2.843ex;" alt="{\displaystyle x^{8}+x^{4}+x^{3}+x^{2}+1}" loading="lazy"></span>, corresponding to the polynomial number 285, with initial root = 0 to obtain generator polynomials.
</p><p>The Reed–Solomon code uses one of 37 different polynomials over <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {F} _{256}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">F</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>256</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mathbb {F} _{256}}</annotation>
</semantics>
</math></span><img src="./3aae762a2df30726681155bd3c3fc1c2036011f9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.118ex; height:2.509ex;" alt="{\displaystyle \mathbb {F} _{256}}" loading="lazy"></span>, with degrees ranging from 7 to 68, depending on how many error correction bytes the code adds. It is implied by the form of Reed–Solomon used (<a href="Reed%E2%80%93Solomon_error_correction#The_BCH_view:_The_codeword_as_a_sequence_of_coefficients" title="Reed–Solomon error correction">systematic BCH view</a>) that these polynomials are all on the form <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \prod _{i=0}^{n-1}(x-\alpha ^{i})}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<munderover>
<mo>∏<!-- ∏ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</munderover>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−<!-- − --></mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msup>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\textstyle \prod _{i=0}^{n-1}(x-\alpha ^{i})}</annotation>
</semantics>
</math></span><img src="./5aab0bb5476a5a9dbafd71ef92c0ade9b1b92180.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.779ex; height:3.509ex;" alt="{\textstyle \prod _{i=0}^{n-1}(x-\alpha ^{i})}" loading="lazy"></span>. However, the rules for selecting the degree <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>n</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle n}</annotation>
</semantics>
</math></span><img src="./a601995d55609f2d9f5e233e36fbe9ea26011b3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" loading="lazy"></span> are specific to the QR standard.
</p><p>For example, the generator polynomial used for the Version 1 QR code (21×21), when 7 error correction bytes are used, is:
<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g(x)=x^{7}+\alpha ^{87}x^{6}+\alpha ^{229}x^{5}+\alpha ^{146}x^{4}+\alpha ^{149}x^{3}+\alpha ^{238}x^{2}+\alpha ^{102}x+\alpha ^{21}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>7</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>87</mn>
</mrow>
</msup>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>6</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>229</mn>
</mrow>
</msup>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>5</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>146</mn>
</mrow>
</msup>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>149</mn>
</mrow>
</msup>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>238</mn>
</mrow>
</msup>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>102</mn>
</mrow>
</msup>
<mi>x</mi>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>21</mn>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle g(x)=x^{7}+\alpha ^{87}x^{6}+\alpha ^{229}x^{5}+\alpha ^{146}x^{4}+\alpha ^{149}x^{3}+\alpha ^{238}x^{2}+\alpha ^{102}x+\alpha ^{21}}</annotation>
</semantics>
</math></span><img src="./582cb33436235b6ae33abef991a263d74cda8ee2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:70.526ex; height:3.176ex;" alt="{\displaystyle g(x)=x^{7}+\alpha ^{87}x^{6}+\alpha ^{229}x^{5}+\alpha ^{146}x^{4}+\alpha ^{149}x^{3}+\alpha ^{238}x^{2}+\alpha ^{102}x+\alpha ^{21}}" loading="lazy"></span>.
</p><p>This is obtained by multiplying the first seven terms:
<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g(x)=(x+1)(x+\alpha )(x+\alpha ^{2})(x+\alpha ^{3})(x+\alpha ^{4})(x+\alpha ^{5})(x+\alpha ^{6})}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mi>α<!-- α --></mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msup>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msup>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>5</mn>
</mrow>
</msup>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<msup>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>6</mn>
</mrow>
</msup>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle g(x)=(x+1)(x+\alpha )(x+\alpha ^{2})(x+\alpha ^{3})(x+\alpha ^{4})(x+\alpha ^{5})(x+\alpha ^{6})}</annotation>
</semantics>
</math></span><img src="./c1f6dab279c5fec4a1f1a22bd75363a413738c4f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:64.568ex; height:3.176ex;" alt="{\displaystyle g(x)=(x+1)(x+\alpha )(x+\alpha ^{2})(x+\alpha ^{3})(x+\alpha ^{4})(x+\alpha ^{5})(x+\alpha ^{6})}" loading="lazy"></span>.
</p><p>The same may also be expressed using decimal coefficients (over <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {F} _{256}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">F</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>256</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mathbb {F} _{256}}</annotation>
</semantics>
</math></span><img src="./3aae762a2df30726681155bd3c3fc1c2036011f9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.118ex; height:2.509ex;" alt="{\displaystyle \mathbb {F} _{256}}" loading="lazy"></span>), as:
<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g(x)=x^{7}+127x^{6}+122x^{5}+154x^{4}+164x^{3}+11x^{2}+68x+117}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>7</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>127</mn>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>6</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>122</mn>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>5</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>154</mn>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>164</mn>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>11</mn>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>68</mn>
<mi>x</mi>
<mo>+</mo>
<mn>117</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle g(x)=x^{7}+127x^{6}+122x^{5}+154x^{4}+164x^{3}+11x^{2}+68x+117}</annotation>
</semantics>
</math></span><img src="./bd41a60990e6197b0f8c8bca21c78ea8172d3710.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:64.956ex; height:3.176ex;" alt="{\displaystyle g(x)=x^{7}+127x^{6}+122x^{5}+154x^{4}+164x^{3}+11x^{2}+68x+117}" loading="lazy"></span>.
</p><p>The highest power of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>x</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle x}</annotation>
</semantics>
</math></span><img src="./87f9e315fd7e2ba406057a97300593c4802b53e4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" loading="lazy"></span> in the polynomial (the degree <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>n</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle n}</annotation>
</semantics>
</math></span><img src="./a601995d55609f2d9f5e233e36fbe9ea26011b3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" loading="lazy"></span>, of the polynomial) determines the number of error correction bytes. In this case, the degree is 7.
</p><p>When discussing the Reed–Solomon code phase there is some risk for confusion, in that the QR ISO/IEC standard uses the term <i>codeword</i> for the elements of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {F} _{256}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">F</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>256</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mathbb {F} _{256}}</annotation>
</semantics>
</math></span><img src="./3aae762a2df30726681155bd3c3fc1c2036011f9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.118ex; height:2.509ex;" alt="{\displaystyle \mathbb {F} _{256}}" loading="lazy"></span>, which with respect to the Reed–Solomon code are <a href="Code#Theory" title="Code">symbols</a>, whereas it uses the term <i>block</i> for what with respect to the Reed–Solomon code are the codewords. The number of data versus error correction bytes within each block depends on (i) the version (side length) of the QR symbol and (ii) the error correction level, of which there are four. The higher the error correction level, the less storage capacity. The following table lists the approximate error correction capability at each of the four levels:
</p>
<table>
<tbody><tr>
<td>Level L (Low)</td>
<td>7% of data bytes can be restored.
</td></tr>
<tr>
<td>Level M (Medium)</td>
<td>15% of data bytes can be restored.
</td></tr>
<tr>
<td>Level Q (Quartile)<sup id="cite_ref-84" class="reference"><a href="#cite_note-84"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup></td>
<td>25% of data bytes can be restored.
</td></tr>
<tr>
<td>Level H (High)</td>
<td>30% of data bytes can be restored.
</td></tr></tbody></table>
<p>In larger QR symbols, the message is broken up into several Reed–Solomon code blocks. The block size is chosen so that no attempt is made at correcting more than 15 errors per block; this limits the complexity of the decoding algorithm. The code blocks are then interleaved together, making it less likely that localized damage to a QR symbol will overwhelm the capacity of any single block.
</p><p>The Version 1 QR symbol with level L error correction, for example, consists of a single error correction block with a total of <b>26 code</b> bytes (made of <b>19</b> message bytes and seven error correction bytes). It can correct up to <b>2</b> byte errors. Hence, this code is known as a <b>(26,19,2)</b> error correction code over <span class="texhtml">GF(2<sup>8</sup>)</span> . It is also sometimes represented in short, as (26,19) code.
</p><p>Due to error correction, it is possible to create artistic QR codes with embellishments to make them more readable or attractive to the human eye, and to incorporate colors, logos, and other features into the QR code block; the embellishments are treated as errors, but the codes still scan correctly.<sup id="cite_ref-85" class="reference"><a href="#cite_note-85"><span class="cite-bracket">[</span>85<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-86" class="reference"><a href="#cite_note-86"><span class="cite-bracket">[</span>86<span class="cite-bracket">]</span></a></sup>
</p><p>It is also possible to design artistic QR codes without reducing the error correction capacity by manipulating the underlying mathematical constructs.<sup id="cite_ref-87" class="reference"><a href="#cite_note-87"><span class="cite-bracket">[</span>87<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-88" class="reference"><a href="#cite_note-88"><span class="cite-bracket">[</span>88<span class="cite-bracket">]</span></a></sup> Image processing algorithms are also used to reduce errors in QR-code.<sup id="cite_ref-89" class="reference"><a href="#cite_note-89"><span class="cite-bracket">[</span>89<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Encoding">Encoding</h3></div>
<div class="mw-heading mw-heading4"><h4 id="Format_information_and_masking">Format information and masking</h4></div>
<p>The format information records two things: the error correction level and the mask pattern used for the symbol. Masking is used to break up patterns in the data area that might confuse a scanner, such as large blank areas or misleading features that look like the locator marks. The mask patterns are defined on a grid that is repeated as necessary to cover the whole symbol. Modules corresponding to the dark areas of the mask are inverted. The 5-bit format information is protected from errors with a <a href="BCH_code" title="BCH code">BCH code</a>, and two complete copies are included in each QR symbol.<sup id="cite_ref-autogenerated1_4-2" class="reference"><a href="#cite_note-autogenerated1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> A (15,5) triple error-correcting BCH code over <span class="texhtml">GF(2<sup>4</sup>)</span> is used, having the generator polynomial <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g(x)=x^{10}+x^{8}+x^{5}+x^{4}+x^{2}+x+1}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>10</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>8</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>5</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle g(x)=x^{10}+x^{8}+x^{5}+x^{4}+x^{2}+x+1}</annotation>
</semantics>
</math></span><img src="./cc625dd562e527c19ca496aade0ffa5a887ac5e5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.63ex; height:3.176ex;" alt="{\displaystyle g(x)=x^{10}+x^{8}+x^{5}+x^{4}+x^{2}+x+1}" loading="lazy"></span>. It can correct at most 3 bit-errors out of the 5 data bits. There are a total of 15 bits in this BCH code (10 bits are added for error correction). This 15-bit code is itself X-ORed with a fixed 15-bit mask pattern (<b>101010000010010</b>) to prevent an all-zero string.
</p>
<div class="mw-heading mw-heading4"><h4 id="Error_correction_bytes">Error correction bytes</h4></div>
<p>To obtain the error correction (EC) bytes for a message "www.wikipedia.org", the following procedure may be carried out:
</p><p>The message is 17 bytes long, hence it can be encoded using a (26,19,2) Reed-Solomon code to fit in a Ver1 (21×21) symbol, which has a maximum capacity of 19 bytes (for L level error correction).
</p><p>The generator polynomial specified for the (26,19,2) code, is:
<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g(x)=x^{7}+127x^{6}+122x^{5}+154x^{4}+164x^{3}+11x^{2}+68x+117}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>7</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>127</mn>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>6</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>122</mn>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>5</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>154</mn>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>164</mn>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>11</mn>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>68</mn>
<mi>x</mi>
<mo>+</mo>
<mn>117</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle g(x)=x^{7}+127x^{6}+122x^{5}+154x^{4}+164x^{3}+11x^{2}+68x+117}</annotation>
</semantics>
</math></span><img src="./bd41a60990e6197b0f8c8bca21c78ea8172d3710.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:64.956ex; height:3.176ex;" alt="{\displaystyle g(x)=x^{7}+127x^{6}+122x^{5}+154x^{4}+164x^{3}+11x^{2}+68x+117}" loading="lazy"></span>,
which may also be written in the form of a matrix of decimal coefficients:
</p>
<pre><b>[1 127 122 154 164 11 68 117]</b>
</pre>
<p>The 17-byte long message "www.wikipedia.org" as hexadecimal coefficients (ASCII values), denoted by M1 through M17 is:
</p>
<pre><b>[77 77 77 2E 77 69 6B 69 70 65 64 69 61 2E 6F 72 67]</b>
</pre>
<p>The encoding mode is "Byte encoding". Hence the 'Enc' field is [0100] (4 bits). The length of the above message is 17 bytes hence 'Len' field is [00010001] (8 bits). The 'End' field is End of message marker [0000] (4 bits).
</p><p>The message code word (without EC bytes) is of the form:
</p>
<pre><b>['Enc' 'Len' w w w . w i k i p e d i a . o r g 'End']</b>
</pre>
<p>Substituting the hexadecimal values, it can be expressed as:
</p>
<pre><b>[4 11 77 77 77 2E 77 69 6B 69 70 65 64 69 61 2E 6F 72 67 0]</b>
</pre>
<p>This is rearranged as 19-byte blocks of 8 bits each:
</p>
<pre><b>[<span style="color:blue">41 17 77 77 72 E7 76 96 B6 97 06 56 46 96 12 E6 F7 26 70</span>]</b>
</pre>
<p>Using the procedure for <a href="Reed%E2%80%93Solomon_error_correction#Constructions_(encoding)" title="Reed–Solomon error correction">Reed-Solomon systematic encoding</a>, the 7 EC bytes obtained (E1 through E7, as shown in the symbol) which are the coefficients (in decimal) of the remainder after polynomial division are:
</p>
<pre><b>[<span style="color:red">174 173 239 6 151 143 37</span>]</b>
</pre>
<p>or in hexadecimal values:
</p>
<pre><b>[<span style="color:red">AE AD EF 06 97 8F 25</span>]</b>
</pre>
<p>These 7 EC bytes are then appended to the 19-byte message. The resulting coded message has 26 bytes (in hexadecimal):
</p>
<pre><b>[<span style="color:blue">41 17 77 77 72 E7 76 96 B6 97 06 56 46 96 12 E6 F7 26 70</span> <span style="color:red">AE AD EF 06 97 8F 25</span>]</b>
</pre>
<p>Note: The bit values shown in the Ver1 QR symbol below do not match with the above values, as the symbol has been masked using a mask pattern (001).
</p>
<div class="mw-heading mw-heading4"><h4 id="Message_placement">Message placement</h4></div>
<p>The message dataset is placed from right to left in a zigzag pattern, as shown below. In larger symbols, this is complicated by the presence of the alignment patterns and the use of multiple interleaved error-correction blocks.
</p>
<ul class="gallery mw-gallery-traditional">
<li class="gallerybox" style="width: 315px">
<div class="thumb" style="width: 310px; height: 230px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Meaning of format information. In the above figure, the format information is protected by a (15,5) BCH code, which can correct up to 3 bit errors. The total length of the code is 15 bits, of which 5 are data bits (2 EC level + 3 mask pattern) and 10 are extra bits for error correction. The <b>format mask pattern</b> for these 15 bits is: [<b>101010000010010</b>]. Note that we map the masked values directly to its meaning here, in contrast to image 4 "Levels & Masks" where the mask pattern numbers are the result of putting the 3rd to 5th mask bit, [<b>101</b>], over the 3rd to 5th format info bit of the QR code.</div>
</li>
<li class="gallerybox" style="width: 315px">
<div class="thumb" style="width: 310px; height: 230px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Message placement within a Ver 1 QR symbol (21×21). The message is encoded using a (255,248) Reed Solomon code (shortened to (26,19) code by using "padding") that can correct up to 2 byte-errors. A total of 26 code-words consist of 7 error-correction bytes, and 17 data bytes, in addition to the "Len" (8 bit field), "Enc" (4 bit field), and "End" (4 bit field). The symbol is capable of level L error correction. The EC level is 01(L), and mask pattern is 001. Hence the first 5 bits of the format information are 01001 (without the format mask). After masking, the 5 bits become 11100, as seen here.</div>
</li>
<li class="gallerybox" style="width: 315px">
<div class="thumb" style="width: 310px; height: 230px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Larger symbol (Ver 3, 29×29) illustrating interleaved blocks. The message has 26 data bytes and is encoded using two Reed-Solomon code blocks. Each block is a (255,233) Reed Solomon code (shortened to (35,13) code), which can correct up to 11 byte-errors in a single burst, containing 13 data bytes and 22 "parity" bytes appended to the data bytes. The two 35-byte Reed-Solomon code blocks are interleaved (resulting in a total of 70 code bytes), so it can correct up to 22 byte-errors. The symbol achieves level H error correction.</div>
</li>
</ul>
<p>The general structure of a QR encoding is as a sequence of 4 bit indicators with payload length dependent on the indicator mode (e.g. byte encoding payload length is dependent on the first byte).<sup id="cite_ref-90" class="reference"><a href="#cite_note-90"><span class="cite-bracket">[</span>90<span class="cite-bracket">]</span></a></sup>
</p>
<table class="wikitable">
<tbody><tr>
<th>Mode indicator</th>
<th>Description</th>
<th>Typical structure '[ type : sizes in bits ]'
</th></tr>
<tr>
<td>1 = 0b0001</td>
<td>Numeric</td>
<td>[0001 : 4] [ Character Count Indicator : variable ] [ Data Bit Stream : 3<span class="frac"><span class="num">1</span>⁄<span class="den">3</span></span> × charcount ]
</td></tr>
<tr>
<td>2 = 0b0010</td>
<td>Alphanumeric</td>
<td>[0010 : 4] [ Character Count Indicator : variable ] [ Data Bit Stream : 5<span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> × charcount ]
</td></tr>
<tr>
<td>4 = 0b0100</td>
<td>Byte encoding</td>
<td>[0100 : 4] [ Character Count Indicator : variable ] [ Data Bit Stream : 8 × charcount ]
</td></tr>
<tr>
<td>8 = 0b1000</td>
<td>Kanji encoding</td>
<td>[1000 : 4] [ Character Count Indicator : variable ] [ Data Bit Stream : 13 × charcount ]
</td></tr>
<tr>
<td>3 = 0b0011</td>
<td>Structured append</td>
<td>[0011 : 4] [ Symbol Position : 4 ] [ Total Symbols: 4 ] [ Parity : 8 ]
</td></tr>
<tr>
<td>7 = 0b0111</td>
<td>ECI</td>
<td>[0111 : 4] [ ECI Assignment number : variable ]
</td></tr>
<tr>
<td>5 = 0b0101</td>
<td>FNC1 in first position</td>
<td>[0101 : 4] [ Numeric/Alphanumeric/Byte/Kanji payload : variable ]
</td></tr>
<tr>
<td>9 = 0b1001</td>
<td>FNC1 in second position</td>
<td>[1001 : 4] [ Application Indicator : 8 ] [ Numeric/Alphanumeric/Byte/Kanji payload : variable ]
</td></tr>
<tr>
<td>0 = 0b0000</td>
<td>End of message</td>
<td>[0000 : 4]
</td></tr></tbody></table>
<small><div>
<dl><dd>Note:
<ul><li>Character Count Indicator depends on how many modules are in a QR code (Symbol Version).</li>
<li>ECI Assignment number Size:
<ul><li>8 × 1 bits if ECI Assignment Bitstream starts with '0'</li>
<li>8 × 2 bits if ECI Assignment Bitstream starts with '10'</li>
<li>8 × 3 bits if ECI Assignment Bitstream starts with '110'</li></ul></li></ul></dd></dl>
</div></small>
<p>Four-bit indicators are used to select the encoding mode and convey other information.
</p>
<table class="wikitable">
<caption>Encoding modes
</caption>
<tbody><tr>
<th>Indicator</th>
<th>Meaning
</th></tr>
<tr>
<td>0001</td>
<td>Numeric encoding (10 bits per 3 digits)
</td></tr>
<tr>
<td>0010</td>
<td>Alphanumeric encoding (11 bits per 2 characters)
</td></tr>
<tr>
<td>0100</td>
<td>Byte encoding (8 bits per character)
</td></tr>
<tr>
<td>1000</td>
<td>Kanji encoding (13 bits per character)
</td></tr>
<tr>
<td>0011</td>
<td>Structured append (used to split a message across multiple QR symbols)
</td></tr>
<tr>
<td>0111</td>
<td><a href="Extended_Channel_Interpretation" title="Extended Channel Interpretation">Extended Channel Interpretation</a> (select alternate character set or encoding)
</td></tr>
<tr>
<td>0101</td>
<td>FNC1 in first position (see <a href="Code_128" title="Code 128">Code 128</a> for more information)
</td></tr>
<tr>
<td>1001</td>
<td>FNC1 in second position
</td></tr>
<tr>
<td>0000</td>
<td>End of message (Terminator)
</td></tr></tbody></table>
<p>Encoding modes can be mixed as needed within a QR symbol. (e.g., a url with a long string of alphanumeric characters )
</p>
<div class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr"><pre>[ Mode Indicator][ Mode bitstream ] --> [ Mode Indicator][ Mode bitstream ] --> etc... --> [ 0000 End of message (Terminator) ]
</pre></div>
<p>After every indicator that selects an encoding mode is a length field that tells how many characters are encoded in that mode. The number of bits in the length field depends on the encoding and the symbol version.
</p>
<table class="wikitable">
<caption>Number of bits in a length field (Character Count Indicator)
</caption>
<tbody><tr>
<th>Encoding</th>
<th>Ver. 1–9</th>
<th>10–26</th>
<th>27–40
</th></tr>
<tr>
<th>Numeric
</th>
<td>10</td>
<td>12</td>
<td>14
</td></tr>
<tr>
<th>Alphanumeric
</th>
<td>9</td>
<td>11</td>
<td>13
</td></tr>
<tr>
<th>Byte
</th>
<td>8</td>
<td>16</td>
<td>16
</td></tr>
<tr>
<th>Kanji
</th>
<td>8</td>
<td>10</td>
<td>12
</td></tr></tbody></table>
<p>Alphanumeric encoding mode stores a message more compactly than the byte mode can, but cannot store lower-case letters and has only a limited selection of punctuation marks, which are sufficient for rudimentary <a href="Web_address" class="mw-redirect" title="Web address">web addresses</a>. Two characters are coded in an 11-bit value by this formula:
</p>
<dl><dd>V = 45 × C<sub>1</sub> + C<sub>2</sub></dd></dl>
<p>This has the exception that the last character in an alphanumeric string with an odd length is read as a 6-bit value instead.
</p>
<table class="wikitable">
<caption>Alphanumeric character codes
</caption>
<tbody><tr>
<th>Code</th>
<th>Character</th>
<th>Code</th>
<th>Character</th>
<th>Code</th>
<th>Character</th>
<th>Code</th>
<th>Character</th>
<th>Code</th>
<th>Character
</th></tr>
<tr>
<td>00</td>
<td>0</td>
<td>09</td>
<td>9</td>
<td>18</td>
<td>I</td>
<td>27</td>
<td>R</td>
<td>36</td>
<td>Space
</td></tr>
<tr>
<td>01</td>
<td>1</td>
<td>10</td>
<td>A</td>
<td>19</td>
<td>J</td>
<td>28</td>
<td>S</td>
<td>37</td>
<td>$
</td></tr>
<tr>
<td>02</td>
<td>2</td>
<td>11</td>
<td>B</td>
<td>20</td>
<td>K</td>
<td>29</td>
<td>T</td>
<td>38</td>
<td>%
</td></tr>
<tr>
<td>03</td>
<td>3</td>
<td>12</td>
<td>C</td>
<td>21</td>
<td>L</td>
<td>30</td>
<td>U</td>
<td>39</td>
<td>*
</td></tr>
<tr>
<td>04</td>
<td>4</td>
<td>13</td>
<td>D</td>
<td>22</td>
<td>M</td>
<td>31</td>
<td>V</td>
<td>40</td>
<td>+
</td></tr>
<tr>
<td>05</td>
<td>5</td>
<td>14</td>
<td>E</td>
<td>23</td>
<td>N</td>
<td>32</td>
<td>W</td>
<td>41</td>
<td>-
</td></tr>
<tr>
<td>06</td>
<td>6</td>
<td>15</td>
<td>F</td>
<td>24</td>
<td>O</td>
<td>33</td>
<td>X</td>
<td>42</td>
<td>.
</td></tr>
<tr>
<td>07</td>
<td>7</td>
<td>16</td>
<td>G</td>
<td>25</td>
<td>P</td>
<td>34</td>
<td>Y</td>
<td>43</td>
<td>/
</td></tr>
<tr>
<td>08</td>
<td>8</td>
<td>17</td>
<td>H</td>
<td>26</td>
<td>Q</td>
<td>35</td>
<td>Z</td>
<td>44</td>
<td>:
</td></tr></tbody></table>
<div class="mw-heading mw-heading3"><h3 id="Decoding_example">Decoding example</h3></div>
<p>The following images offer more information about the QR code.
</p>
<ul class="gallery mw-gallery-traditional" style="max-width: 865px;">
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<div class="gallerytext">1 – Introduction</div>
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<div class="thumb" style="width: 160px; height: 130px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">2 – Structure</div>
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<div class="thumb" style="width: 160px; height: 130px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">3 – Layout & Encoding</div>
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<div class="gallerytext">4 – Levels & Masks</div>
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<div class="thumb" style="width: 160px; height: 130px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">5 – Protocols</div>
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<div class="mw-heading mw-heading2"><h2 id="Variants">Variants</h2></div>
<div class="mw-heading mw-heading3"><h3 id="Model_1">Model 1</h3></div>
<p><i>Model 1 QR code</i> is an older version of the specification. It is visually similar to the widely seen model 2 codes, but lacks alignment patterns. Differences are in the bottom right corner, and in the midsections of the bottom and right edges are additional functional regions.
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<div class="gallerytext">Model 1 QR code example</div>
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<div class="thumb" style="width: 130px; height: 130px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Model 1 QR code functional regions</div>
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<div class="mw-heading mw-heading3"><h3 id="Micro_QR_code">Micro QR code </h3></div>
<p>Micro QR code is a smaller version of the QR code standard for applications where symbol size is limited. There are four different versions (sizes) of Micro QR codes: the smallest is 11×11 modules; the largest can hold 35 numeric characters,<sup id="cite_ref-91" class="reference"><a href="#cite_note-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup> or 21 <a href="ASCII" title="ASCII">ASCII</a> alphanumeric characters, or 15 bytes (120 bits).
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<div class="gallerytext">Micro QR code example</div>
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<div class="thumb" style="width: 130px; height: 130px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Micro QR code functional regions</div>
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<div class="mw-heading mw-heading3"><h3 id="Rectangular_Micro_QR_Code">Rectangular Micro QR Code</h3></div>
<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Rectangular_Micro_QR_Code" title="Rectangular Micro QR Code">Rectangular Micro QR Code</a></div>
<p>Rectangular Micro QR Code (also known as rMQR Code) is a two-dimensional (2D) matrix barcode invented and standardized in 2022 by Denso Wave as ISO/IEC 23941. rMQR Code is designed as a rectangular variation of the QR code and has the same parameters and applications as original QR codes; however, rMQR Code is more suitable for rectangular areas, and has a difference between width and height up to 19 in the R7x139 version.
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<div class="gallerytext">Rectangular Micro QR Code (rMQR Code) example</div>
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</ul>
<div class="mw-heading mw-heading3"><h3 id="iQR_code">iQR code</h3></div>
<p>iQR code is an alternative to existing square QR codes developed by Denso Wave. iQR codes can be created in square or rectangular formations; this is intended for situations where a longer and narrower rectangular shape is more suitable, such as on cylindrical objects. iQR codes can fit the same amount of information in 30% less space. There are 61 versions of square iQR codes, and 15 versions of rectangular codes. For squares, the minimum size is 9 × 9 modules; rectangles have a minimum of 19 × 5 modules. iQR codes add error correction level S, which allows for 50% error correction.<sup id="cite_ref-92" class="reference"><a href="#cite_note-92"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup> iQR Codes had not been given an ISO/IEC specification as of 2015, and only proprietary Denso Wave products could create or read iQR codes.<sup id="cite_ref-93" class="reference"><a href="#cite_note-93"><span class="cite-bracket">[</span>93<span class="cite-bracket">]</span></a></sup>
</p>
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<li class="gallerybox" style="width: 287px">
<div class="thumb" style="width: 282px; height: 130px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">iQR code example</div>
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</ul>
<div class="mw-heading mw-heading3"><h3 id="Secure_QR_code">Secure QR code</h3></div>
<p>Secure Quick Response (SQR) code is a QR code that contains a "private data" segment after the terminator instead of the specified filler bytes "ec 11".<sup id="cite_ref-94" class="reference"><a href="#cite_note-94"><span class="cite-bracket">[</span>94<span class="cite-bracket">]</span></a></sup> This private data segment must be deciphered with an encryption key. This can be used to store private information and to manage a company's internal information.<sup id="cite_ref-95" class="reference"><a href="#cite_note-95"><span class="cite-bracket">[</span>95<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Frame_QR">Frame QR</h3></div>
<p>Frame QR is a variant of the QR code standard which arranges the code in a frame around a central empty area. It is intended to be used in applications where an image, artwork, or branding is desired to be part of the code.<sup id="cite_ref-96" class="reference"><a href="#cite_note-96"><span class="cite-bracket">[</span>96<span class="cite-bracket">]</span></a></sup>
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<div class="gallerytext">Frame QR example</div>
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<div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Frame QR code example with a circular frame and the <a href="Wikipedia_logo" title="Wikipedia logo">Wikipedia logo</a> composed into its interior</div>
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</ul>
<div class="mw-heading mw-heading3"><h3 id="HCC2D">HCC2D</h3></div>
<p>Researchers have proposed a new High Capacity Colored 2-Dimensional (HCC2D) Code, which builds upon a QR code basis for preserving the QR robustness to distortions and uses colors for increasing data density (as of 2014 it is still in the prototyping phase). The HCC2D code specification is described in details in Querini <i>et al.</i> (2011),<sup id="cite_ref-97" class="reference"><a href="#cite_note-97"><span class="cite-bracket">[</span>97<span class="cite-bracket">]</span></a></sup> while techniques for color classification of HCC2D code cells are described in detail in Querini and <a href="Giuseppe_F._Italiano" title="Giuseppe F. Italiano">Italiano</a> (2014),<sup id="cite_ref-98" class="reference"><a href="#cite_note-98"><span class="cite-bracket">[</span>98<span class="cite-bracket">]</span></a></sup> which is an extended version of Querini and Italiano (2013).<sup id="cite_ref-Querini_and_Italiano_(2013)_99-0" class="reference"><a href="#cite_note-Querini_and_Italiano_(2013)-99"><span class="cite-bracket">[</span>99<span class="cite-bracket">]</span></a></sup>
</p><p>Introducing colors into QR codes requires addressing additional issues. In particular, during QR code reading only the brightness information is taken into account, while HCC2D codes have to cope with chromatic distortions during the decoding phase. In order to ensure adaptation to chromatic distortions that arise in each scanned code, HCC2D codes make use of an additional field: the Color Palette Pattern. This is because color cells of a Color Palette Pattern are supposed to be distorted in the same way as color cells of the Encoding Region. Replicated color palettes are used for training machine-learning classifiers.
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<div class="gallerytext">HCC2D code examples: (a) 4-color HCC2D code and (b) 8-color HCC2D code</div>
</li>
</ul>
<div class="mw-heading mw-heading3"><h3 id="Accessible_QR_(AQR)">Accessible QR (AQR)</h3></div>
<p>Accessible QR (AQR) is a type of QR code that combines a standard QR code with a dot-dash pattern positioned around one corner of the code to provide product information for people who are blind and partially sighted. The codes, announce product categories and product details such as instructions, ingredients, safety warnings, and recycling information. The data is structured for the needs of users who are blind or partially sighted and offers larger text or audio output. It can read QR codes from a metre away, activating the smartphone's accessibility features like VoiceOver to announce product details.
</p>
<div class="mw-heading mw-heading2"><h2 id="License">License</h2></div>
<p>The use of QR code technology is freely licensed as long as users follow the standards for QR code documented with <a href="Japanese_Industrial_Standards" title="Japanese Industrial Standards">JIS</a> or <a href="International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a>/<a href="International_Electrotechnical_Commission" title="International Electrotechnical Commission">IEC</a>. Non-standardized codes may require special licensing.<sup id="cite_ref-qrpatent01_100-0" class="reference"><a href="#cite_note-qrpatent01-100"><span class="cite-bracket">[</span>100<span class="cite-bracket">]</span></a></sup>
</p><p>Denso Wave owns a number of patents on QR code technology, but has chosen to exercise them in a limited fashion.<sup id="cite_ref-qrpatent01_100-1" class="reference"><a href="#cite_note-qrpatent01-100"><span class="cite-bracket">[</span>100<span class="cite-bracket">]</span></a></sup> In order to promote widespread usage of the technology Denso Wave chose to waive its rights to a key patent in its possession for <i>standardized</i> codes only.<sup id="cite_ref-qrstandard1_17-1" class="reference"><a href="#cite_note-qrstandard1-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> In the US, the granted QR code patent, 5726435, expired on March 14, 2015. In Japan, the corresponding patent, 2938338, expired on March 14, 2014. The <a href="European_Patent_Office" title="European Patent Office">European Patent Office</a> granted patent 0672994 to Denso Wave, which was then validated into <a href="France" title="France">French</a>, UK, and German patents, all of which expired in March 2015.<sup id="cite_ref-101" class="reference"><a href="#cite_note-101"><span class="cite-bracket">[</span>101<span class="cite-bracket">]</span></a></sup>
</p><p>The text <i>QR Code</i> itself is a <a href="Registered_trademark" class="mw-redirect" title="Registered trademark">registered trademark</a> and <a href="Wordmark" title="Wordmark">wordmark</a> of Denso Wave Incorporated.<sup id="cite_ref-qrtrademark01_102-0" class="reference"><a href="#cite_note-qrtrademark01-102"><span class="cite-bracket">[</span>102<span class="cite-bracket">]</span></a></sup> In UK, the trademark is registered as E921775, the term <i>QR Code</i>, with a filing date of 3 September 1998.<sup id="cite_ref-qrtrademarkuk_103-0" class="reference"><a href="#cite_note-qrtrademarkuk-103"><span class="cite-bracket">[</span>103<span class="cite-bracket">]</span></a></sup> The UK version of the trademark is based on the Kabushiki Kaisha Denso (DENSO CORPORATION) trademark, filed as Trademark 000921775, the term <i>QR Code</i>, on 3 September 1998 and registered on 16 December 1999 with the European Union OHIM (Office for Harmonization in the Internal Market).<sup id="cite_ref-qrtrademarkeu_104-0" class="reference"><a href="#cite_note-qrtrademarkeu-104"><span class="cite-bracket">[</span>104<span class="cite-bracket">]</span></a></sup>
The U.S. Trademark for the term <i>QR Code</i> is Trademark 2435991 and was filed on 29 September 1998 with an amended registration date of 13 March 2001, assigned to Denso Corporation.<sup id="cite_ref-qrtrademarkus_105-0" class="reference"><a href="#cite_note-qrtrademarkus-105"><span class="cite-bracket">[</span>105<span class="cite-bracket">]</span></a></sup> In South Korea, trademark application filed on 18 November 2011 was refused on 20 March 2012, because the <a href="Korean_Intellectual_Property_Office" title="Korean Intellectual Property Office">Korean Intellectual Property Office</a> viewed that the phrase was <a href="Generic_trademark" title="Generic trademark">genericized</a> among South Korean people to refer to matrix barcodes in general.<sup id="cite_ref-qrtrademarkkr_106-0" class="reference"><a href="#cite_note-qrtrademarkkr-106"><span class="cite-bracket">[</span>106<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Risks">Risks</h2></div>
<p>The only context in which common QR codes can carry executable data is the URL data type. These URLs may host <a href="JavaScript" title="JavaScript">JavaScript</a> code, which can be used to exploit vulnerabilities in applications on the host system, such as the reader, the web browser, or the image viewer, since a reader will typically send the data to the application associated with the data type used by the QR code.
</p><p>In the case of no software exploits, malicious QR codes combined with a permissive reader can still put a computer's contents and user's privacy at risk. This practice is known as "attagging", a <a href="Portmanteau" class="mw-redirect" title="Portmanteau">portmanteau</a> of "attack tagging".<sup id="cite_ref-Wired_107-0" class="reference"><a href="#cite_note-Wired-107"><span class="cite-bracket">[</span>107<span class="cite-bracket">]</span></a></sup> They are easily created and can be affixed over legitimate QR codes.<sup id="cite_ref-108" class="reference"><a href="#cite_note-108"><span class="cite-bracket">[</span>108<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-IEEEQRRisks_109-0" class="reference"><a href="#cite_note-IEEEQRRisks-109"><span class="cite-bracket">[</span>109<span class="cite-bracket">]</span></a></sup> On a smartphone, the reader's permissions may allow use of the camera, full Internet access, read/write contact data, <a href="GPS" class="mw-redirect" title="GPS">GPS</a>, read browser history, read/write local storage, and global system changes.<sup id="cite_ref-110" class="reference"><a href="#cite_note-110"><span class="cite-bracket">[</span>110<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-111" class="reference"><a href="#cite_note-111"><span class="cite-bracket">[</span>111<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-112" class="reference"><a href="#cite_note-112"><span class="cite-bracket">[</span>112<span class="cite-bracket">]</span></a></sup>
</p><p>Risks include linking to dangerous web sites with browser exploits, enabling the microphone/camera/GPS, and then streaming those feeds to a remote server, analysis of sensitive data (passwords, files, contacts, transactions),<sup id="cite_ref-113" class="reference"><a href="#cite_note-113"><span class="cite-bracket">[</span>113<span class="cite-bracket">]</span></a></sup> and sending email/<a href="Short_Message_Service" class="mw-redirect" title="Short Message Service">SMS</a>/IM messages or packets for <a href="Denial-of-service_attack" title="Denial-of-service attack">DDoS</a> as part of a <a href="Botnet" title="Botnet">botnet</a>, corrupting privacy settings, stealing identity,<sup id="cite_ref-114" class="reference"><a href="#cite_note-114"><span class="cite-bracket">[</span>114<span class="cite-bracket">]</span></a></sup> and even containing malicious logic themselves such as JavaScript<sup id="cite_ref-115" class="reference"><a href="#cite_note-115"><span class="cite-bracket">[</span>115<span class="cite-bracket">]</span></a></sup> or a virus.<sup id="cite_ref-116" class="reference"><a href="#cite_note-116"><span class="cite-bracket">[</span>116<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-117" class="reference"><a href="#cite_note-117"><span class="cite-bracket">[</span>117<span class="cite-bracket">]</span></a></sup> These actions could occur in the background while the user is only seeing the reader opening a seemingly harmless web page.<sup id="cite_ref-118" class="reference"><a href="#cite_note-118"><span class="cite-bracket">[</span>118<span class="cite-bracket">]</span></a></sup> In Russia, a malicious QR code caused phones that scanned it to send premium texts at a fee of <a href="United_States_dollar" title="United States dollar">$</a>6 each.<sup id="cite_ref-Wired_107-1" class="reference"><a href="#cite_note-Wired-107"><span class="cite-bracket">[</span>107<span class="cite-bracket">]</span></a></sup> QR codes have also been linked to scams in which stickers are placed on <a href="Parking_meters" class="mw-redirect" title="Parking meters">parking meters</a> and other devices, posing as quick payment options, as seen in <a href="Austin%2C_Texas" title="Austin, Texas">Austin</a>, <a href="San_Antonio" title="San Antonio">San Antonio</a> and <a href="Boston" title="Boston">Boston</a>, among other cities across the United States and Australia.<sup id="cite_ref-119" class="reference"><a href="#cite_note-119"><span class="cite-bracket">[</span>119<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-120" class="reference"><a href="#cite_note-120"><span class="cite-bracket">[</span>120<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-121" class="reference"><a href="#cite_note-121"><span class="cite-bracket">[</span>121<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Aztec_Code" title="Aztec Code">Aztec Code</a></li>
<li><a href="Data_Matrix" title="Data Matrix">Data Matrix</a></li>
<li><a href="High_Capacity_Color_Barcode" title="High Capacity Color Barcode">High Capacity Color Barcode</a></li>
<li><a href="JAB_Code" title="JAB Code">JAB Code</a></li>
<li><a href="MaxiCode" title="MaxiCode">MaxiCode</a></li>
<li><a href="PDF417" title="PDF417">PDF417</a></li>
<li><a href="QRpedia" title="QRpedia">QRpedia</a></li>
<li><a href="SnapTag" title="SnapTag">SnapTag</a></li>
<li><a href="SPARQCode" title="SPARQCode">SPARQCode</a></li>
<li><a href="Touchatag" title="Touchatag">Touchatag</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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</style><cite id="CITEREFHara2024" class="citation interview cs1"><a href="Masahiro_Hara" title="Masahiro Hara">Hara, Masahiro</a> (1 October 2024). <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=w5ebcowAJD8&t=2049">"I used to hate QR codes. But they're actually genius"</a> (Interview). Interviewed by <a href="Derek_Muller" title="Derek Muller">Muller, Derek</a>. 34:09<span class="reference-accessdate">. Retrieved <span class="nowrap">1 October</span> 2024</span>. <q>The biggest feature of QR codes is that they can be read quickly. It's called Quick Response because it reacts quickly.</q></cite></span>
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<ul><li><cite class="citation book cs1"><i>BS ISO/IEC 18004:2006. Information technology. Automatic identification and data capture techniques. Bar code symbology. QR Code</i>. <a href="Geneva" title="Geneva">Geneva</a>: <a href="International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a>/<a href="International_Electrotechnical_Commission" title="International Electrotechnical Commission">IEC</a>. 2000. p. 114. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/60816353">60816353</a>.</cite></li>
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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>
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<div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:QR_codes" class="extiw external" title="commons:Category:QR codes">QR codes</a></span>.</div></div>
</div>
<ul><li><a href="https://en.wikiversity.org/wiki/Reed%E2%80%93Solomon_codes_for_coders" class="extiw external" title="v:Reed–Solomon codes for coders">Reed Solomon Codes for Coders</a> – an elaborate tutorial on Wikiversity, covering both QR code structure and the Reed Solomon codes used to encode the data.</li></ul>
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</style><div id="Barcodes453" style="font-size:114%;margin:0 4em"><a href="Barcode" title="Barcode">Barcodes</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Linear barcodes</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="KarTrak" title="KarTrak">Automatic Car Identification</a></li>
<li><a href="Code_11" title="Code 11">Code 11</a></li>
<li><a href="Code_39" title="Code 39">Code 39</a></li>
<li><a href="Code_93" title="Code 93">Code 93</a></li>
<li><a href="Code_128" title="Code 128">Code 128</a></li>
<li><a href="Codabar" title="Codabar">Codabar</a></li>
<li><a href="International_Article_Number" title="International Article Number">European Article Number</a></li>
<li><a href="GS1_DataBar" class="mw-redirect" title="GS1 DataBar">GS1 DataBar</a></li>
<li><a href="Industrial_2_of_5" title="Industrial 2 of 5">Industrial 2 of 5</a></li>
<li><a href="Interleaved_2_of_5" title="Interleaved 2 of 5">Interleaved 2 of 5</a></li>
<li><a href="ITF-14" class="mw-redirect" title="ITF-14">ITF-14</a></li>
<li><a href="Matrix_2_of_5" title="Matrix 2 of 5">Matrix 2 of 5</a></li>
<li><a href="MSI_Barcode" title="MSI Barcode">MSI Barcode</a></li>
<li><a href="Patch_Code" title="Patch Code">Patch Code</a></li>
<li><a href="Pharmacode" title="Pharmacode">Pharmacode</a></li>
<li><a href="Plessey_Code" title="Plessey Code">Plessey</a></li>
<li><a href="Telepen" title="Telepen">Telepen</a></li>
<li><a href="Universal_Product_Code" title="Universal Product Code">UPC</a></li></ul>
</div></td><td class="noviewer navbox-image" rowspan="9" style="width:1px;padding:0 0 0 2px"><div><table>
<tbody><tr><td><span typeof="mw:File"></span></td>
</tr><tr><td><a href="Universal_Product_Code" title="Universal Product Code">UPC-A</a></td>
</tr><tr><td><span typeof="mw:File"></span></td>
</tr><tr><td><a href="MaxiCode" title="MaxiCode">MaxiCode</a></td>
</tr></tbody></table></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Mail" title="Mail">Post office</a> barcodes</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="CPC_Binary_Barcode" title="CPC Binary Barcode">CPC Binary Barcode</a></li>
<li><a href="Facing_Identification_Mark" title="Facing Identification Mark">Facing Identification Mark</a></li>
<li><a href="PostBar" title="PostBar">PostBar</a></li>
<li><a href="POSTNET" title="POSTNET">POSTNET</a></li>
<li><a href="RM4SCC" title="RM4SCC">RM4SCC</a></li>
<li><a href="Intelligent_Mail_barcode" title="Intelligent Mail barcode">Intelligent Mail barcode</a></li>
<li><a href="Postal_Alpha_Numeric_Encoding_Technique" title="Postal Alpha Numeric Encoding Technique">PLANET</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">2D barcodes (stacked)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Codablock" title="Codablock">Codablock</a></li>
<li><a href="GS1_DataBar" class="mw-redirect" title="GS1 DataBar">GS1 DataBar</a></li>
<li><a href="MicroPDF417" title="MicroPDF417">MicroPDF417</a></li>
<li><a href="PDF417" title="PDF417">PDF417</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">2D barcodes (<a href="Matrix_(mathematics)" title="Matrix (mathematics)">matrix</a>)</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Aztec_Code" title="Aztec Code">Aztec Code</a></li>
<li><a href="Data_Matrix" title="Data Matrix">Data Matrix</a> (<a href="Semacode" title="Semacode">Semacode</a>)</li>
<li><a href="DotCode" title="DotCode">DotCode</a></li>
<li><a href="Han_Xin_code" title="Han Xin code">Han Xin code</a></li>
<li><a href="JAB_Code" title="JAB Code">JAB Code</a></li>
<li><a href="MaxiCode" title="MaxiCode">MaxiCode</a></li>
<li><a href="Rectangular_Micro_QR_Code" title="Rectangular Micro QR Code">rMQR Code</a></li>
<li><a href="Boxing_barcode" title="Boxing barcode">Boxing</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Polar_coordinate_system" title="Polar coordinate system">Polar coordinate</a> barcodes</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="MaxiCode" title="MaxiCode">MaxiCode</a></li>
<li><a href="ShotCode" title="ShotCode">ShotCode</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="High_Capacity_Color_Barcode" title="High Capacity Color Barcode">High Capacity Color Barcode (Microsoft Tag)</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Technological issues</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Barcode_library" title="Barcode library">Barcode library</a></li>
<li><a href="Barcode_printer" title="Barcode printer">Barcode printer</a></li>
<li><a href="Barcode_reader" title="Barcode reader">Barcode reader</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other data tags</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Radio-frequency_identification" title="Radio-frequency identification">RFID</a></li>
<li><a href="Bokode" title="Bokode">Bokode</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Supply_chain_management" title="Supply chain management">Supply chain management</a></li>
<li><a href="Object_hyperlinking" title="Object hyperlinking">Object hyperlinking</a></li>
<li><a href="Matrix_(mathematics)" title="Matrix (mathematics)">Matrix</a></li>
<li><a href="Mobile_tagging" title="Mobile tagging">Mobile tagging</a></li>
<li><a href="CueCat" title="CueCat">CueCat</a></li></ul>
</div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3"><div>
<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> Category</li>
<li><span class="noviewer" typeof="mw:File"><span title="Commons page"></span></span> <a href="https://commons.wikimedia.org/wiki/Category:Barcode" class="extiw external" title="commons:Category:Barcode">Commons</a></li></ul>
</div></td></tr></tbody></table></div>
<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="International_Organization_for_Standardization_(ISO)_standards364" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="International_Organization_for_Standardization_(ISO)_standards364" style="font-size:114%;margin:0 4em"><a href="International_Organization_for_Standardization" title="International Organization for Standardization">International Organization for Standardization</a> (ISO) standards</div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>List of <a href="List_of_ISO_standards" title="List of ISO standards">ISO standards</a> – <a href="List_of_ISO_romanizations" title="List of ISO romanizations">ISO romanizations</a> – <a href="List_of_IEC_standards" title="List of IEC standards">IEC standards</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">1–9999</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="ISO_1" title="ISO 1">1</a></li>
<li><a href="ISO_2" title="ISO 2">2</a></li>
<li><a href="Renard_series" title="Renard series">3</a></li>
<li><a href="ISO_4" title="ISO 4">4</a></li>
<li><a href="Film_speed" title="Film speed">6</a></li>
<li><a href="British_Standard_Pipe" title="British Standard Pipe">7</a></li>
<li><a href="ISO_9" title="ISO 9">9</a></li>
<li><a href="A440_(pitch_standard)" title="A440 (pitch standard)">16</a></li>
<li><a href="Renard_series" title="Renard series">17</a></li>
<li><a href="ISO_31" title="ISO 31">31</a>
<ul><li><a href="ISO_31-0" title="ISO 31-0">-0</a></li>
<li><a href="ISO_31-1" title="ISO 31-1">-1</a></li>
<li><a href="ISO_31-3" title="ISO 31-3">-3</a></li>
<li><a href="ISO_31-4" title="ISO 31-4">-4</a></li>
<li><a href="ISO_31-5" title="ISO 31-5">-5</a></li>
<li><a href="ISO_31-6" title="ISO 31-6">-6</a></li>
<li><a href="ISO_31-7" title="ISO 31-7">-7</a></li>
<li><a href="ISO_31-8" title="ISO 31-8">-8</a></li>
<li><a href="ISO_31-9" class="mw-redirect" title="ISO 31-9">-9</a></li>
<li><a href="ISO_31-10" title="ISO 31-10">-10</a></li>
<li><a href="ISO_31-11" title="ISO 31-11">-11</a></li>
<li><a href="ISO_31-12" class="mw-redirect" title="ISO 31-12">-12</a></li>
<li><a href="ISO_31-13" class="mw-redirect" title="ISO 31-13">-13</a></li></ul></li>
<li><a href="ISO_metric_screw_thread" title="ISO metric screw thread">68-1</a></li>
<li><a href="ISO_128" title="ISO 128">128</a></li>
<li><a href="ISO_216" title="ISO 216">216</a></li>
<li><a href="ISO_217" title="ISO 217">217</a></li>
<li><a href="Equal-loudness_contour" title="Equal-loudness contour">226</a></li>
<li><a href="British_Standard_Pipe" title="British Standard Pipe">228</a></li>
<li><a href="ISO_233" title="ISO 233">233</a></li>
<li><a href="ISO_259" title="ISO 259">259</a></li>
<li><a href="ISO_metric_screw_thread" title="ISO metric screw thread">261</a></li>
<li><a href="ISO_metric_screw_thread" title="ISO metric screw thread">262</a></li>
<li><a href="Kappa_number" title="Kappa number">302</a></li>
<li><a href="Vicat_softening_point" title="Vicat softening point">306</a></li>
<li><a href="Hazard_symbol#Ionizing_radiation_symbol" title="Hazard symbol">361</a></li>
<li><a href="Power_take-off" title="Power take-off">500</a></li>
<li><a href="Hot_shoe" title="Hot shoe">518</a></li>
<li><a href="Prontor-Compur" title="Prontor-Compur">519</a></li>
<li><a href="ISO_639" title="ISO 639">639</a>
<ul><li><a href="ISO_639-1" title="ISO 639-1">-1</a></li>
<li><a href="ISO_639-2" title="ISO 639-2">-2</a></li>
<li><a href="ISO_639-3" title="ISO 639-3">-3</a></li>
<li><a href="ISO_639-5" title="ISO 639-5">-5</a></li>
<li><a href="ISO_639-6" title="ISO 639-6">-6</a></li></ul></li>
<li><a href="ISO/IEC_646" title="ISO/IEC 646">646</a></li>
<li><a href="ISO_657" title="ISO 657">657</a></li>
<li><a href="ISO_668" title="ISO 668">668</a></li>
<li><a href="ISO_690" title="ISO 690">690</a></li>
<li><a href="ISO_704" title="ISO 704">704</a></li>
<li><a href="ISO_732" title="ISO 732">732</a></li>
<li><a href="Antimagnetic_watch" title="Antimagnetic watch">764</a></li>
<li><a href="Hole_punch" title="Hole punch">838</a></li>
<li><a href="ISO_843" title="ISO 843">843</a></li>
<li><a href="ISO_860" title="ISO 860">860</a></li>
<li><a href="ISO_898" title="ISO 898">898</a></li>
<li><a href="ISO_965" title="ISO 965">965</a></li>
<li><a href="ISO_999" title="ISO 999">999</a></li>
<li><a href="ISO_1000" title="ISO 1000">1000</a></li>
<li><a href="Magnetic_ink_character_recognition" title="Magnetic ink character recognition">1004</a></li>
<li><a href="135_film" title="135 film">1007</a></li>
<li><a href="OCR-A" title="OCR-A">1073-1</a></li>
<li><a href="OCR-B" title="OCR-B">1073-2</a></li>
<li><a href="Longitudinal_redundancy_check" title="Longitudinal redundancy check">1155</a></li>
<li><a href="Shock-resistant_watch#ISO_1413_shock-resistant_standard" title="Shock-resistant watch">1413</a></li>
<li><a href="ALGOL_60" title="ALGOL 60">1538</a></li>
<li><a href="ISO_1629" title="ISO 1629">1629</a></li>
<li><a href="ISO_1745" title="ISO 1745">1745</a></li>
<li><a href="COBOL" title="COBOL">1989</a></li>
<li><a href="ISO_2014" title="ISO 2014">2014</a></li>
<li><a href="ISO_2015" title="ISO 2015">2015</a></li>
<li><a href="ISO/IEC_2022" title="ISO/IEC 2022">2022</a></li>
<li><a href="ISO_2033" title="ISO 2033">2033</a></li>
<li><a href="ISO_2047" title="ISO 2047">2047</a></li>
<li><a href="ISBN" title="ISBN">2108</a></li>
<li><a href="ISO_2145" title="ISO 2145">2145</a></li>
<li><a href="ISO_2146" title="ISO 2146">2146</a></li>
<li><a href="Film_speed" title="Film speed">2240</a></li>
<li><a href="Water_Resistant_mark" title="Water Resistant mark">2281</a></li>
<li><a href="International_Standard_Atmosphere" title="International Standard Atmosphere">2533</a></li>
<li><a href="ISO_2709" title="ISO 2709">2709</a></li>
<li><a href="ISO_2711" title="ISO 2711">2711</a></li>
<li><a href="Film_speed" title="Film speed">2720</a></li>
<li><a href="ISO_2788" title="ISO 2788">2788</a></li>
<li><a href="ISO_2848" title="ISO 2848">2848</a></li>
<li><a href="ISO_2852" title="ISO 2852">2852</a></li>
<li><a href="ISO_2921" title="ISO 2921">2921</a></li>
<li><a href="126_film" title="126 film">3029</a></li>
<li><a href="ISO_3103" title="ISO 3103">3103</a></li>
<li><a href="ISO_3166" title="ISO 3166">3166</a>
<ul><li><a href="ISO_3166-1" title="ISO 3166-1">-1</a></li>
<li><a href="ISO_3166-2" title="ISO 3166-2">-2</a></li>
<li><a href="ISO_3166-3" title="ISO 3166-3">-3</a></li></ul></li>
<li><a href="ISSN" title="ISSN">3297</a></li>
<li><a href="ISO_3307" title="ISO 3307">3307</a></li>
<li><a href="O-ring" title="O-ring">3601</a></li>
<li><a href="Kunrei-shiki_romanization" class="mw-redirect" title="Kunrei-shiki romanization">3602</a></li>
<li><a href="ISO_3864" title="ISO 3864">3864</a></li>
<li><a href="International_Standard_Recording_Code" title="International Standard Recording Code">3901</a></li>
<li><a href="FDI_World_Dental_Federation_notation" title="FDI World Dental Federation notation">3950</a></li>
<li><a href="ISO_3977" title="ISO 3977">3977</a></li>
<li><a href="ISO_4031" title="ISO 4031">4031</a></li>
<li><a href="ISO_4157" class="mw-redirect" title="ISO 4157">4157</a></li>
<li><a href="ISO_4165" title="ISO 4165">4165</a></li>
<li><a href="ISO_4217" title="ISO 4217">4217</a></li>
<li><a href="ISO/IEC_4909" title="ISO/IEC 4909">4909</a></li>
<li><a href="ISO/IEC_5218" title="ISO/IEC 5218">5218</a></li>
<li><a href="ISO_5426" title="ISO 5426">5426</a></li>
<li><a href="ISO_5427" title="ISO 5427">5427</a></li>
<li><a href="ISO_5428" title="ISO 5428">5428</a></li>
<li><a href="Accuracy_and_precision" title="Accuracy and precision">5725</a></li>
<li><a href="ISO_5775" title="ISO 5775">5775</a></li>
<li><a href="ISO_5776" title="ISO 5776">5776</a></li>
<li><a href="Film_speed" title="Film speed">5800</a></li>
<li><a href="Flowchart" title="Flowchart">5807</a></li>
<li><a href="ISO_5964" title="ISO 5964">5964</a></li>
<li><a href="International_Securities_Identification_Number" title="International Securities Identification Number">6166</a></li>
<li><a href="ISO_6344" title="ISO 6344">6344</a></li>
<li><a href="ISO_6346" title="ISO 6346">6346</a></li>
<li><a href="Minimal_BASIC" title="Minimal BASIC">6373</a></li>
<li><a href="ISO_6385" title="ISO 6385">6385</a></li>
<li><a href="Water_Resistant_mark" title="Water Resistant mark">6425</a></li>
<li><a href="ANSI_escape_code" title="ANSI escape code">6429</a></li>
<li><a href="ISO_6438" title="ISO 6438">6438</a></li>
<li><a href="ISO/IEC_6523" title="ISO/IEC 6523">6523</a></li>
<li><a href="ISO_6709" title="ISO 6709">6709</a></li>
<li><a href="ISO_6943" title="ISO 6943">6943</a></li>
<li><a href="ISO_7001" title="ISO 7001">7001</a></li>
<li><a href="ISO_7002" title="ISO 7002">7002</a></li>
<li><a href="ISO_7010" title="ISO 7010">7010</a></li>
<li><a href="ISO_7027" title="ISO 7027">7027</a></li>
<li><a href="ISO/IEC_7064" title="ISO/IEC 7064">7064</a></li>
<li><a href="Pinyin" title="Pinyin">7098</a></li>
<li><a href="Pascal_(programming_language)" title="Pascal (programming language)">7185</a></li>
<li><a href="ISO_7200" title="ISO 7200">7200</a></li>
<li><a href="OSI_model" title="OSI model">7498</a>
<ul><li><a href="OSI_model" title="OSI model">-1</a></li></ul></li>
<li><a href="ISO_7637" title="ISO 7637">7637</a></li>
<li><a href="ISO_7736" title="ISO 7736">7736</a></li>
<li><a href="ISO/IEC_7810" title="ISO/IEC 7810">7810</a></li>
<li><a href="ISO/IEC_7811" title="ISO/IEC 7811">7811</a></li>
<li><a href="ISO/IEC_7812" title="ISO/IEC 7812">7812</a></li>
<li><a href="ISO/IEC_7813" title="ISO/IEC 7813">7813</a></li>
<li><a href="ISO/IEC_7816" title="ISO/IEC 7816">7816</a></li>
<li><a href="Graphical_Kernel_System" title="Graphical Kernel System">7942</a></li>
<li><a href="ISO_8000" title="ISO 8000">8000</a></li>
<li><a href="On-board_diagnostics" title="On-board diagnostics">8093</a></li>
<li><a href="ISO_8178" title="ISO 8178">8178</a></li>
<li><a href="Fuel_oil" title="Fuel oil">8217</a></li>
<li><a href="ISO_8373" class="mw-redirect" title="ISO 8373">8373</a></li>
<li><a href="ISO_8501-1" title="ISO 8501-1">8501-1</a></li>
<li><a href="FTAM" title="FTAM">8571</a></li>
<li><a href="ISO_8583" title="ISO 8583">8583</a></li>
<li><a href="ISO_8601" title="ISO 8601">8601</a></li>
<li><a href="Open_Document_Architecture" title="Open Document Architecture">8613</a></li>
<li><a href="Computer_Graphics_Metafile" title="Computer Graphics Metafile">8632</a></li>
<li><a href="Graphical_Kernel_System" title="Graphical Kernel System">8651</a></li>
<li><a href="ISO/IEC_8652" title="ISO/IEC 8652">8652</a></li>
<li><a href="ISO_8691" title="ISO 8691">8691</a></li>
<li><a href="Graphical_Kernel_System" title="Graphical Kernel System">8805/8806</a></li>
<li><a href="Language_of_Temporal_Ordering_Specification" title="Language of Temporal Ordering Specification">8807</a></li>
<li><a href="Automotive_fuse" title="Automotive fuse">8820-5</a></li>
<li><a href="ISO/IEC_8859" title="ISO/IEC 8859">8859</a>
<ul><li><a href="ISO/IEC_8859-1" title="ISO/IEC 8859-1">-1</a></li>
<li><a href="ISO/IEC_8859-2" title="ISO/IEC 8859-2">-2</a></li>
<li><a href="ISO/IEC_8859-3" title="ISO/IEC 8859-3">-3</a></li>
<li><a href="ISO/IEC_8859-4" title="ISO/IEC 8859-4">-4</a></li>
<li><a href="ISO/IEC_8859-5" title="ISO/IEC 8859-5">-5</a></li>
<li><a href="ISO/IEC_8859-6" title="ISO/IEC 8859-6">-6</a></li>
<li><a href="ISO/IEC_8859-7" title="ISO/IEC 8859-7">-7</a></li>
<li><a href="ISO/IEC_8859-8" title="ISO/IEC 8859-8">-8</a></li>
<li><a href="ISO-8859-8-I" title="ISO-8859-8-I">-8-I</a></li>
<li><a href="ISO/IEC_8859-9" title="ISO/IEC 8859-9">-9</a></li>
<li><a href="ISO/IEC_8859-10" title="ISO/IEC 8859-10">-10</a></li>
<li><a href="ISO/IEC_8859-11" title="ISO/IEC 8859-11">-11</a></li>
<li><a href="ISO/IEC_8859-12" class="mw-redirect" title="ISO/IEC 8859-12">-12</a></li>
<li><a href="ISO/IEC_8859-13" title="ISO/IEC 8859-13">-13</a></li>
<li><a href="ISO/IEC_8859-14" title="ISO/IEC 8859-14">-14</a></li>
<li><a href="ISO/IEC_8859-15" title="ISO/IEC 8859-15">-15</a></li>
<li><a href="ISO/IEC_8859-16" title="ISO/IEC 8859-16">-16</a></li></ul></li>
<li><a href="Standard_Generalized_Markup_Language" title="Standard Generalized Markup Language">8879</a></li>
<li><a href="ISO_9000_family" title="ISO 9000 family">9000/9001</a></li>
<li><a href="ASMO_449" title="ASMO 449">9036</a></li>
<li><a href="SQL" title="SQL">9075</a></li>
<li><a href="ISO/IEC_9126" title="ISO/IEC 9126">9126</a></li>
<li><a href="On-board_diagnostics" title="On-board diagnostics">9141</a></li>
<li><a href="Salt_spray_test" title="Salt spray test">9227</a></li>
<li><a href="ISO_9241" title="ISO 9241">9241</a></li>
<li><a href="File_Allocation_Table" title="File Allocation Table">9293</a></li>
<li><a href="Fiber_Distributed_Data_Interface" title="Fiber Distributed Data Interface">9314</a></li>
<li><a href="ISO_9362" title="ISO 9362">9362</a></li>
<li><a href="Shoe_size" title="Shoe size">9407</a></li>
<li><a href="CHILL" title="CHILL">9496</a></li>
<li><a href="Manufacturing_Message_Specification" title="Manufacturing Message Specification">9506</a></li>
<li><a href="ISO/IEC_9529" title="ISO/IEC 9529">9529</a></li>
<li><a href="ISO_9564" title="ISO 9564">9564</a></li>
<li><a href="PHIGS" title="PHIGS">9592/9593</a></li>
<li><a href="X.500" title="X.500">9594</a></li>
<li><a href="ISO_9660" title="ISO 9660">9660</a></li>
<li><a href="ISO/IEC_9797-1" title="ISO/IEC 9797-1">9797-1</a></li>
<li><a href="ISO_9897" title="ISO 9897">9897</a></li>
<li><a href="ANSI_C" title="ANSI C">9899</a></li>
<li><a href="POSIX" title="POSIX">9945</a></li>
<li><a href="Romanization_of_Georgian" title="Romanization of Georgian">9984</a></li>
<li><a href="Romanization_of_Armenian" title="Romanization of Armenian">9985</a></li>
<li><a href="ISO/IEC_9995" title="ISO/IEC 9995">9995</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">10000–19999</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="ISO_10006" title="ISO 10006">10006</a></li>
<li><a href="ISO_10007" title="ISO 10007">10007</a></li>
<li><a href="ISO/IEC_10116" title="ISO/IEC 10116">10116</a></li>
<li><a href="Whirlpool_(hash_function)" title="Whirlpool (hash function)">10118-3</a></li>
<li><a href="ISO_10160" title="ISO 10160">10160</a></li>
<li><a href="ISO_10161" title="ISO 10161">10161</a></li>
<li><a href="Guidelines_for_the_Definition_of_Managed_Objects" title="Guidelines for the Definition of Managed Objects">10165</a></li>
<li><a href="Document_Style_Semantics_and_Specification_Language" title="Document Style Semantics and Specification Language">10179</a></li>
<li><a href="Pascal_(programming_language)#ISO/IEC_10206:1990_Extended_Pascal" title="Pascal (programming language)">10206</a></li>
<li><a href="ISO_10218" title="ISO 10218">10218</a></li>
<li><a href="Full_BASIC" title="Full BASIC">10279</a></li>
<li><a href="ISO_10303" title="ISO 10303">10303</a>
<ul><li><a href="EXPRESS_(data_modeling_language)" title="EXPRESS (data modeling language)">-11</a></li>
<li><a href="ISO_10303-21" title="ISO 10303-21">-21</a></li>
<li><a href="ISO_10303-22" title="ISO 10303-22">-22</a></li>
<li><a href="ISO_10303-28" title="ISO 10303-28">-28</a></li>
<li><a href="STEP-NC" title="STEP-NC">-238</a></li></ul></li>
<li><a href="Market_Identifier_Code" title="Market Identifier Code">10383</a></li>
<li><a href="ArmSCII" title="ArmSCII">10585</a></li>
<li><a href="IS-IS" title="IS-IS">10589</a></li>
<li><a href="ISO_10628" title="ISO 10628">10628</a></li>
<li><a href="Universal_Coded_Character_Set" title="Universal Coded Character Set">10646</a></li>
<li><a href="Torx" title="Torx">10664</a></li>
<li><a href="RM-ODP" title="RM-ODP">10746</a></li>
<li><a href="Multibus" title="Multibus">10861</a></li>
<li><a href="International_Standard_Music_Number" title="International Standard Music Number">10957</a></li>
<li><a href="ISO_10962" title="ISO 10962">10962</a></li>
<li><a href="ISO/IEC_10967" title="ISO/IEC 10967">10967</a></li>
<li><a href="ISO/IEEE_11073" title="ISO/IEEE 11073">11073</a></li>
<li><a href="ISO_11170" title="ISO 11170">11170</a></li>
<li><a href="MPEG-1" title="MPEG-1">11172</a></li>
<li><a href="ISO/IEC_11179" title="ISO/IEC 11179">11179</a></li>
<li><a href="ISO/IEC_11404" title="ISO/IEC 11404">11404</a></li>
<li><a href="JBIG" title="JBIG">11544</a></li>
<li><a href="ISO_11783" title="ISO 11783">11783</a></li>
<li><a href="ISO_11784_and_ISO_11785" title="ISO 11784 and ISO 11785">11784</a></li>
<li><a href="ISO_11784_and_ISO_11785" title="ISO 11784 and ISO 11785">11785</a></li>
<li><a href="ISO/IEC_11801" title="ISO/IEC 11801">11801</a></li>
<li><a href="Trusted_Platform_Module" title="Trusted Platform Module">11889</a></li>
<li><a href="CAN_bus#CAN_lower-layer_standards" title="CAN bus">11898</a></li>
<li><a href="ISO_11940" title="ISO 11940">11940</a> (<a href="ISO_11940-2" title="ISO 11940-2">-2</a>)</li>
<li><a href="ISO/TR_11941" title="ISO/TR 11941">11941</a></li>
<li><a href="ISO/TR_11941" title="ISO/TR 11941">11941 (TR)</a></li>
<li><a href="ISO_11992" title="ISO 11992">11992</a></li>
<li><a href="ISO_12006" title="ISO 12006">12006</a></li>
<li><a href="DICOM" title="DICOM">12052</a></li>
<li><a href="ISO/IEC_TR_12182" title="ISO/IEC TR 12182">12182</a></li>
<li><a href="ISO/IEC_12207" title="ISO/IEC 12207">12207</a></li>
<li><a href="TIFF/EP" title="TIFF/EP">12234-2</a></li>
<li><a href="Linguistic_categories#ISO_12620_(ISO_TC37_Data_Category_Registry,_ISOcat)" title="Linguistic categories">12620</a></li>
<li><a href="Prolog" title="Prolog">13211</a>
<ul><li><a href="Prolog" title="Prolog">-1</a></li>
<li><a href="Prolog" title="Prolog">-2</a></li></ul></li>
<li><a href="Isofix" title="Isofix">13216</a></li>
<li><a href="Topic_map" title="Topic map">13250</a></li>
<li><a href="ISO_13399" title="ISO 13399">13399</a></li>
<li><a href="ISO_13406-2" title="ISO 13406-2">13406-2</a></li>
<li><a href="110_film" title="110 film">13450</a></li>
<li><a href="ISO_13485" title="ISO 13485">13485</a></li>
<li><a href="ISO_13490" title="ISO 13490">13490</a></li>
<li><a href="ISO_13567" title="ISO 13567">13567</a></li>
<li><a href="Z_notation" title="Z notation">13568</a></li>
<li><a href="ISO_13584" title="ISO 13584">13584</a></li>
<li><a href="International_Bank_Account_Number" title="International Bank Account Number">13616</a></li>
<li><a href="ISLISP" title="ISLISP">13816</a></li>
<li><a href="MPEG-2" title="MPEG-2">13818</a></li>
<li><a href="ISO_14000_family" title="ISO 14000 family">14000</a></li>
<li><a href="ISO_14031" title="ISO 14031">14031</a></li>
<li><a href="ISO_14224" title="ISO 14224">14224</a></li>
<li><a href="PDF/UA" title="PDF/UA">14289</a></li>
<li><a href="Horsepower" title="Horsepower">14396</a></li>
<li><a href="ISO/IEC_14443" title="ISO/IEC 14443">14443</a></li>
<li><a href="MPEG-4" title="MPEG-4">14496</a>
<ul><li><a href="MPEG-4_Part_2" title="MPEG-4 Part 2">-2</a></li>
<li><a href="MPEG-4_Part_3" title="MPEG-4 Part 3">-3</a></li>
<li><a href="Delivery_Multimedia_Integration_Framework" title="Delivery Multimedia Integration Framework">-6</a></li>
<li><a href="Advanced_Video_Coding" title="Advanced Video Coding">-10</a></li>
<li><a href="MPEG-4_Part_11" title="MPEG-4 Part 11">-11</a></li>
<li><a href="ISO_base_media_file_format" title="ISO base media file format">-12</a></li>
<li><a href="MP4_file_format" title="MP4 file format">-14</a></li>
<li><a href="MP4_file_format" title="MP4 file format">-17</a></li>
<li><a href="MP4_file_format" title="MP4 file format">-20</a></li></ul></li>
<li><a href="ISO_14617" title="ISO 14617">14617</a></li>
<li><a href="ISO_14644" title="ISO 14644">14644</a></li>
<li><a href="STEP-NC" title="STEP-NC">14649</a></li>
<li><a href="ISO/IEC_14651" title="ISO/IEC 14651">14651</a></li>
<li><a href="ISO_14698" title="ISO 14698">14698</a></li>
<li><a href="Software_maintenance" title="Software maintenance">14764</a></li>
<li><a href="C%2B%2B" title="C++">14882</a></li>
<li><a href="ISO_14971" title="ISO 14971">14971</a></li>
<li><a href="ISO_15022" title="ISO 15022">15022</a></li>
<li><a href="ISO_15189" title="ISO 15189">15189</a></li>
<li><a href="ISO/IEC_15288" title="ISO/IEC 15288">15288</a></li>
<li><a href="Ada_Semantic_Interface_Specification" title="Ada Semantic Interface Specification">15291</a></li>
<li><a href="ISO_15398" title="ISO 15398">15398</a></li>
<li><a href="Common_Criteria" title="Common Criteria">15408</a></li>
<li><a href="JPEG_2000" title="JPEG 2000">15444</a>
<ul><li><a href="Motion_JPEG_2000" title="Motion JPEG 2000">-3</a></li>
<li><a href="JPIP" title="JPIP">-9</a></li></ul></li>
<li><a href="HTML" title="HTML">15445</a></li>
<li><a href="PDF417" title="PDF417">15438</a></li>
<li><a href="ISO/IEC_15504" title="ISO/IEC 15504">15504</a></li>
<li><a href="International_Standard_Identifier_for_Libraries_and_Related_Organizations" title="International Standard Identifier for Libraries and Related Organizations">15511</a></li>
<li><a href="ISO_15686" title="ISO 15686">15686</a></li>
<li><a href="ISO/IEC_15693" title="ISO/IEC 15693">15693</a></li>
<li><a href="International_Standard_Audiovisual_Number" title="International Standard Audiovisual Number">15706</a>
<ul><li><a href="International_Standard_Audiovisual_Number" title="International Standard Audiovisual Number">-2</a></li></ul></li>
<li><a href="International_Standard_Musical_Work_Code" title="International Standard Musical Work Code">15707</a></li>
<li><a href="ISO/IEC_15897" title="ISO/IEC 15897">15897</a></li>
<li><a href="ISO_15919" title="ISO 15919">15919</a></li>
<li><a href="ISO_15924" title="ISO 15924">15924</a></li>
<li><a href="ISO_15926" title="ISO 15926">15926</a></li>
<li><a href="ISO_15926_WIP" title="ISO 15926 WIP">15926 WIP</a></li>
<li><a href="PDF/X" title="PDF/X">15930</a></li>
<li><a href="MPEG-7" title="MPEG-7">15938</a></li>
<li><a href="MaxiCode" title="MaxiCode">16023</a></li>
<li><a href="ECMAScript" title="ECMAScript">16262</a></li>
<li><a href="Quality_function_deployment" title="Quality function deployment">16355-1</a></li>
<li><a href="Mixed_raster_content" title="Mixed raster content">16485</a></li>
<li><a href="PDF/VT" title="PDF/VT">16612-2</a></li>
<li><a href="ISO_16750" title="ISO 16750">16750</a></li>
<li><a href="IATF_16949" title="IATF 16949">16949 (TS)</a></li>
<li><a href="ISO/IEC_17024" title="ISO/IEC 17024">17024</a></li>
<li><a href="ISO/IEC_17025" title="ISO/IEC 17025">17025</a></li>
<li><a href="ISO_17100" title="ISO 17100">17100</a></li>
<li><a href="Open_Virtualization_Format" title="Open Virtualization Format">17203</a></li>
<li><a href="SDMX" title="SDMX">17369</a></li>
<li><a href="Legal_Entity_Identifier" title="Legal Entity Identifier">17442</a></li>
<li><a href="COLLADA" title="COLLADA">17506</a></li>
<li><a href="ISO/IEC_27002" title="ISO/IEC 27002">17799</a></li>
<li><a href="ISO/IEC_18014" title="ISO/IEC 18014">18014</a></li>
<li><a href="JPEG_XL" title="JPEG XL">18181</a></li>
<li><a href="ISO_18245" title="ISO 18245">18245</a></li>
<li><a href="Process_Specification_Language" title="Process Specification Language">18629</a></li>
<li><a href="SoftWare_Hash_IDentifier" title="SoftWare Hash IDentifier">18760</a></li>
<li><a href="Photographic_Activity_Test" title="Photographic Activity Test">18916</a></li>
<li><a href="PDF/A" title="PDF/A">19005</a></li>
<li><a href="ISO_19011" title="ISO 19011">19011</a></li>
<li><a href="ISO_19092" title="ISO 19092">19092</a>
<ul><li><a href="ISO_19092-1" class="mw-redirect" title="ISO 19092-1">-1</a></li>
<li><a href="ISO_19092-2" class="mw-redirect" title="ISO 19092-2">-2</a></li></ul></li>
<li><a href="ISO_19114" title="ISO 19114">19114</a></li>
<li><a href="Geospatial_metadata#ISO_19115:_Geographic_information_–_Metadata" title="Geospatial metadata">19115</a></li>
<li><a href="Simple_Features" title="Simple Features">19125</a></li>
<li><a href="Geography_Markup_Language#ISO_19136" title="Geography Markup Language">19136</a></li>
<li><a href="Shoe_size" title="Shoe size">19407</a></li>
<li><a href="ISO_19439" title="ISO 19439">19439</a></li>
<li><a href="Common_Object_Request_Broker_Architecture" title="Common Object Request Broker Architecture">19500</a></li>
<li><a href="Unified_Modeling_Language" title="Unified Modeling Language">19501</a></li>
<li><a href="Meta-Object_Facility" title="Meta-Object Facility">19502</a></li>
<li><a href="XML_Metadata_Interchange" title="XML Metadata Interchange">19503</a></li>
<li><a href="Unified_Modeling_Language" title="Unified Modeling Language">19505</a></li>
<li><a href="Knowledge_Discovery_Metamodel" title="Knowledge Discovery Metamodel">19506</a></li>
<li><a href="Object_Constraint_Language" title="Object Constraint Language">19507</a></li>
<li><a href="Meta-Object_Facility" title="Meta-Object Facility">19508</a></li>
<li><a href="XML_Metadata_Interchange" title="XML Metadata Interchange">19509</a></li>
<li><a href="Business_Process_Model_and_Notation" title="Business Process Model and Notation">19510</a></li>
<li><a href="ISO_19600" title="ISO 19600">19600</a></li>
<li><a href="ISO/IEC_19752" title="ISO/IEC 19752">19752</a></li>
<li><a href="RELAX_NG" title="RELAX NG">19757</a></li>
<li><a href="ISO/IEC_19770" title="ISO/IEC 19770">19770</a></li>
<li><a href="X3D" title="X3D">19775-1</a></li>
<li><a href="ISO/IEC_19794-5" title="ISO/IEC 19794-5">19794-5</a></li>
<li><a href="Cloud_Infrastructure_Management_Interface" title="Cloud Infrastructure Management Interface">19831</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">20000–29999</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="ISO/IEC_20000" title="ISO/IEC 20000">20000</a></li>
<li><a href="ISO_20022" title="ISO 20022">20022</a></li>
<li><a href="ISO_20121" title="ISO 20121">20121</a></li>
<li><a href="ISO_20400" title="ISO 20400">20400</a></li>
<li><a href="Open_Data_Protocol" title="Open Data Protocol">20802</a></li>
<li><a href="Han_Xin_code" title="Han Xin code">20830</a></li>
<li><a href="MPEG-21" title="MPEG-21">21000</a></li>
<li><a href="ISO_21001" title="ISO 21001">21001</a></li>
<li><a href="International_Standard_Text_Code" title="International Standard Text Code">21047</a></li>
<li><a href="JPEG_XS" title="JPEG XS">21122</a></li>
<li><a href="ISO_21500" title="ISO 21500">21500</a></li>
<li><a href="JSON" title="JSON">21778</a></li>
<li><a href="ISO/IEC_21827" title="ISO/IEC 21827">21827</a></li>
<li><a href="ISO_22000" title="ISO 22000">22000</a></li>
<li><a href="ECMAScript" title="ECMAScript">22275</a></li>
<li><a href="ISO_22300" title="ISO 22300">22300</a></li>
<li><a href="ISO_22301" title="ISO 22301">22301</a></li>
<li><a href="ISO_22395" title="ISO 22395">22395</a></li>
<li><a href="ECMAScript_for_XML" title="ECMAScript for XML">22537</a></li>
<li><a href="MPEG-A" title="MPEG-A">23000</a></li>
<li><a href="MPEG-D" title="MPEG-D">23003</a></li>
<li><a href="MPEG-H" title="MPEG-H">23008</a></li>
<li><a href="Dynamic_Adaptive_Streaming_over_HTTP" title="Dynamic Adaptive Streaming over HTTP">23009</a></li>
<li><a href="Versatile_Video_Coding" title="Versatile Video Coding">23090-3</a></li>
<li><a href="MPEG-G" title="MPEG-G">23092</a></li>
<li><a href="Essential_Video_Coding" title="Essential Video Coding">23094-1</a></li>
<li><a href="LCEVC" title="LCEVC">23094-2</a></li>
<li><a href="C_Sharp_(programming_language)" title="C Sharp (programming language)">23270</a></li>
<li><a href="Common_Language_Infrastructure" title="Common Language Infrastructure">23271</a></li>
<li><a href="Linux_Standard_Base" title="Linux Standard Base">23360</a></li>
<li><a href="Rectangular_Micro_QR_Code" title="Rectangular Micro QR Code">23941</a></li>
<li><a href="PDF/E" title="PDF/E">24517</a></li>
<li><a href="Lexical_Markup_Framework" title="Lexical Markup Framework">24613</a></li>
<li><a href="ISO-TimeML" title="ISO-TimeML">24617</a></li>
<li><a href="Common_Logic" title="Common Logic">24707</a></li>
<li><a href="MicroPDF417" title="MicroPDF417">24728</a></li>
<li><a href="ISO_25178" title="ISO 25178">25178</a></li>
<li><a href="ISO_25964" title="ISO 25964">25964</a></li>
<li><a href="ISO_26000" title="ISO 26000">26000</a></li>
<li><a href="ISO_26262" title="ISO 26262">26262</a></li>
<li><a href="OpenDocument" title="OpenDocument">26300</a></li>
<li><a href="Digital_object_identifier" title="Digital object identifier">26324</a></li>
<li><a href="ISO/IEC_27000_family" title="ISO/IEC 27000 family">27000 series</a></li>
<li><a href="ISO/IEC_27000" title="ISO/IEC 27000">27000</a></li>
<li><a href="ISO/IEC_27001" title="ISO/IEC 27001">27001</a></li>
<li><a href="ISO/IEC_27002" title="ISO/IEC 27002">27002</a></li>
<li><a href="ISO/IEC_27005" title="ISO/IEC 27005">27005</a></li>
<li><a href="ISO/IEC_27006" title="ISO/IEC 27006">27006</a></li>
<li><a href="International_Standard_Name_Identifier" title="International Standard Name Identifier">27729</a></li>
<li><a href="ISO_28000" title="ISO 28000">28000</a></li>
<li>29110</li>
<li><a href="Requirements_engineering" title="Requirements engineering">29148</a></li>
<li><a href="JPEG_XR" title="JPEG XR">29199-2</a></li>
<li><a href="Office_Open_XML" title="Office Open XML">29500</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">30000+</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Ruby_(programming_language)" title="Ruby (programming language)">30170</a></li>
<li><a href="ISO_31000" title="ISO 31000">31000</a></li>
<li><a href="PDF" title="PDF">32000</a></li>
<li><a href="ISO_37001" title="ISO 37001">37001</a></li>
<li><a href="ISO/IEC_38500" title="ISO/IEC 38500">38500</a></li>
<li><a href="Graph_Query_Language" title="Graph Query Language">39075</a></li>
<li><a href="MathML" title="MathML">40314</a></li>
<li><a href="Web_Content_Accessibility_Guidelines" title="Web Content Accessibility Guidelines">40500</a></li>
<li><a href="ISO/IEC_42010" title="ISO/IEC 42010">42010</a></li>
<li><a href="ISO_45001" title="ISO 45001">45001</a></li>
<li><a href="ISO_50001" title="ISO 50001">50001</a></li>
<li><a href="ISO_55000" title="ISO 55000">55000</a></li>
<li><a href="ISO_56000" title="ISO 56000">56000</a></li>
<li><a href="ISO/IEC_80000" title="ISO/IEC 80000">80000</a></li></ul>
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<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> Category</li></ul>
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