A Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunication (CDMA)[1] and satellite navigation (GPS).[2] Gold codes are named after Robert Gold.[3] Gold codes have bounded small cross-correlations within a set, which is useful when multiple devices are broadcasting in the same range. A set of Gold code sequences consists of sequences each one with a period of .
A set of Gold codes can be generated with the following steps. Pick two maximum length sequences of the same length such that their absolute cross-correlation is less than or equal to , where is the size of the LFSR used to generate the maximum length sequence (Gold '67). The set of the exclusive-ors of the two sequences in their various phases (i.e. translated into all relative positions) is a set of Gold codes. The highest absolute cross-correlation in this set of codes is for even and for odd .
The exclusive or of two 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.[4]
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