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A `!Gold code`!, also known as `!Gold sequence`!, is a type of binary `F33f`_`[sequence`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Sequence]`_`f, used in `F33f`_`[telecommunications`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Telecommunications]`_`f (`F33f`_`[CDMA`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=CDMA]`_`f)`:cite-ref-george-hamid-miller-2008-1-0[`F5bf`_`[1`#cite-note-george-hamid-miller-2008-1]`_`f] and satellite navigation (`F33f`_`[GPS`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=GPS]`_`f).`:cite-ref-gps-2009-2-0[`F5bf`_`[2`#cite-note-gps-2009-2]`_`f] Gold codes are named after Robert Gold.`:cite-ref-gold-2011-3-0[`F5bf`_`[3`#cite-note-gold-2011-3]`_`f]`:cite-ref-gold-1967-4-0[`F5bf`_`[4`#cite-note-gold-1967-4]`_`f] Gold codes have bounded small `F33f`_`[cross-correlations`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Cross-correlation]`_`f within a set, which is useful when multiple devices are broadcasting in the same frequency range. A set of Gold code sequences consists of 2`*n`* + 1 sequences each one with a period of 2`*n`* − 1.

A set of Gold codes can be generated with the following steps. Pick two `F33f`_`[maximum length sequences`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Maximum_length_sequence]`_`f of the same length 2`*n`* − 1 such that their absolute `F33f`_`[cross-correlation`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Cross-correlation]`_`f is less than or equal to 2(`*n`*+2)/2, where `*n`* is the size of the `F33f`_`[linear-feedback shift register`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Linear-feedback_shift_register]`_`f used to generate the maximum length sequence.`:cite-ref-gold-1967-4-1[`F5bf`_`[4`#cite-note-gold-1967-4]`_`f] The set of the 2`*n`* − 1 `F33f`_`[exclusive-ors`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Exclusive-or]`_`f of the two sequences in their various phases (i.e. translated into all relative positions) together with the two maximum length sequences form a set of 2`*n`* + 1 Gold code sequences. The highest absolute cross-correlation in this set of codes is 2(`*n`*+2)/2 + 1 for even `*n`* and 2(`*n`*+1)/2 + 1 for odd `*n`*.

The `F33f`_`[exclusive or`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Exclusive_or]`_`f of two different Gold codes from the same set is another Gold code in some phase.

Within a set of Gold codes about half of the codes are balanced – the number of ones and zeros differs by only one.`:cite-ref-holmes-2007-5-0[`F5bf`_`[5`#cite-note-holmes-2007-5]`_`f]

Gold codes are used in `F33f`_`[GPS`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=GPS]`_`f. The `F33f`_`[GPS C/A`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=GPS_signals]`_`f ranging codes are Gold codes of period 1,023.

>>Contents

• `F0af`_`[See also`#see-also]`_`f

• `F0af`_`[References`#references]`_`f

• `F0af`_`[Further reading`#further-reading]`_`f

-─

>>See also

• `F33f`_`[Hadamard code`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Hadamard_code]`_`f

• `F33f`_`[JPL code`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=JPL_code]`_`f

• `F33f`_`[Kasami code`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Kasami_code]`_`f

• `F33f`_`[Zadoff–Chu sequence`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Zadoff–Chu_sequence]`_`f

• `F33f`_`[Complementary sequences`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Complementary_sequences]`_`f

• `F33f`_`[Space Network`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Space_Network]`_`f – a NASA system that uses Gold codes

>>References

`:cite-note-george-hamid-miller-2008-1`!1.`! `F0af`_`[↑`#cite-ref-george-hamid-miller-2008-1-0]`_`f `:citerefgeorgehamidmiller2001`aGeorge, Maria; Hamid, Mujtaba; Miller, Andy (2001-01-10). "Gold Code Generators in Virtex Devices" (PDF). `*Virtex Series, Virtex-II Series, and Spartan-II family`* (Application note). 1.1. `F33f`_`[Xilinx`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Xilinx]`_`f. XAPP217. Archived from the original (PDF) on 2008-07-05. (9 pages)

`:cite-note-gps-2009-2`!2.`! `F0af`_`[↑`#cite-ref-gps-2009-2-0]`_`f "Transmitted GPS Signals". `*The GPS System`*. kowoma GPS. 2009-04-19. Archived from the original on 2012-08-04.

`:cite-note-gold-2011-3`!3.`! `F0af`_`[↑`#cite-ref-gold-2011-3-0]`_`f "Robert Gold, BS, MS, Ph.D." Robert Gold Comm Systems. 2011. Archived from the original on 2017-06-24. Retrieved 2008-07-18.

`:cite-note-gold-1967-4`!4.`! `F0af`_`[↑`#cite-ref-gold-1967-4-0]`_`f `:citerefgold1967`aGold, Robert (October 1967). "Optimal binary sequences for spread spectrum multiplexing". `*`F33f`_`[IEEE Transactions on Information Theory`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=IEEE_Transactions_on_Information_Theory]`_`f`* (Correspondence). IT-13 (4): 619–621. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1109/TIT.1967.1054048.

`:cite-note-holmes-2007-5`!5.`! `F0af`_`[↑`#cite-ref-holmes-2007-5-0]`_`f `:citerefholmes2007`aHolmes, Jack K. (2007-06-30). `*Spread Spectrum Systems for GNSS and Wireless Communications`*. GNSS Technology and Applications Series. Vol. 45. Artech House. p. 100. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-1-59693-083-4.

>>Further reading

• `:citerefgoiser1998`aGoiser, Alois M. J. (1998). "4.3.2. Gold-Folgen" [Gold sequences]. `*Handbuch der Spread-Spectrum Technik`* [`*Handbook of the spread-spectrum technique`*] (in German) (1 ed.). Vienna, Austria: `F33f`_`[Springer Verlag`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Springer_Verlag]`_`f. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 3-211-83080-4.

• `:citerefskaughjelmstad1985`aSkaug, Reidar; Hjelmstad, Jens F. (1985). "Coding for bandwidth spreading". In Flood, J. E.; Hughes, C. J. (eds.). `*Spread Spectrum in Communication`*. IEE Telecommunications Series. Vol. 12 (1 ed.). London, UK: Peter Peregrinus Ltd. / `F33f`_`[The Institution of Electrical Engineers`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=The_Institution_of_Electrical_Engineers]`_`f. pp. 82–. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 0-86341-034-0. (xii+201+1 pages)

• `:citerefrudolphrudolph2011`aRudolph, Dietmar; Rudolph, Matthias (2011-04-12). "46.3.1 Gold-Codes". `*Modulationsverfahren`* (PDF) (in German). Cottbus, Germany: `F33f`_`[Brandenburg University of Technology`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Brandenburg_University_of_Technology]`_`f (BTU). pp. 212–214. Archived (PDF) from the original on 2021-06-16. Retrieved 2021-06-14. (xiv+225 pages)

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