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 2m + 1 sequences each one with a period of 2m − 1.
All 2m + 1 sequences are balanced and contain either 2m−1 ones and 2m−1 − 1 zeros or 2m−1 − 1 ones and 2m−1 zeros.