Pick two m-sequences of the same length n, such that their cross-correlation takes just three values. The set of the n exclusive-ors of the two sequences in their various phases (i.e. translated into all relative positions), together with the two n-sequences themselves, is a set of Gold codes.

The exclusive or of two Gold codes is another Gold code in some phase.

A set of gold sequences consist of 2^m + 1 sequences each one with a period of 2^m − 1.

All 2^m + 1 sequences are balanced and contain either 2^m−1 ones and 2^m−1 − 1 zeros or 2^m−1 − 1 ones and 2^m−1 zeros.

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