A Gold code, also known as Gold sequence, is a type of binary sequence used in telecommunications (CDMA) and satellite navigation (GPS). Gold codes are named after Robert Gold. 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 linear-feedback shift register used to generate the maximum-length sequence. The set of the 2n 1 exclusive-ors of the two sequences in their various phases (i.e. translated into all relative positions) together with the two maximum-length sequences form a set of 2n + 1 Gold code sequences. 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 oddn.

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 balancedthe number of ones and zeros differs by only one.

Gold codes are used in GPS. The GPS C/A ranging codes are Gold codes of period 1,023.

See also

• Hadamard code

• Hamming code

• JPL code

• Kasami code

• Zadoff–Chu sequence

• Complementary sequences

• Space Network – a NASA system that uses Gold codes

References

Further reading

• (xii+201+1 pages)

• (xiv+225 pages)

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