# Gold code

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 frequency range. A set of Gold code sequences consists of 2n − 1 sequences each one with a period of 2n − 1.

A set of Gold codes can be generated with the following steps. Pick two maximum length sequences of the same length 2n − 1 such that their absolute cross-correlation is less than or equal to 2(n+2)/2, where n is the size of the LFSR used to generate the maximum length sequence (Gold '67). The set of the 2n − 1 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 2(n+2)/2 + 1 for even n and 2(n+1)/2 + 1 for odd n.

The exclusive or 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.[4]