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These concepts can be extended naturally to vectorial Boolean functions by considering their output bits (coordinates) individually, or more thoroughly, by looking at the set of all linear functions of output bits, known as its components.cite-ref-2-6-1[6] The set of Walsh transforms of the components is known as a linear approximation table (LAT)cite-ref-3-13-0[13]cite-ref-4-14-0[14] or correlation matrix;cite-ref-15[15]cite-ref-16[16] it describes the correlation between different linear combinations of input and output bits. The set of autocorrelation coefficients of the components is the autocorrelation table,cite-ref-4-14-1[14] related by a Walsh transform of the componentscite-ref-17[17] to the more widely used difference distribution table (DDT)cite-ref-3-13-1[13]cite-ref-4-14-2[14] which lists the correlations between differences in input and output bits (see also: S-box).

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