Gold code

This article is about binary codes used in telecommunications and GPS. For the authentification codes used to command a launch of nuclear weapons, see Gold Codes.

A Gold code is a set of binary sequences, used in telecommunication and satellite navigation (GPS). 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.

References

• Gold, R. Optimal binary sequences for spread spectrum multiplexing (Corresp.), IEEE Transactions on Information Theory, volume 13,number 4,pages 619--621, 1967.

See also

• Kasami code
• Complementary sequences