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]}^{[4]} 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 2^{n} + 1 sequences each one with a period of 2^{n} − 1.

A set of Gold codes can be generated with the following steps. Pick two maximum length sequences of the same length 2^{n} − 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 (Gold '67). The set of the 2^{n} − 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 2^{n} + 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 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.^{[5]}

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

## See also

- Kasami code
- Hadamard code
- Zadoff–Chu sequence
- Complementary sequences
- Space Network – a NASA system that uses Gold codes

## References

**^**George, M.; Hamid, M.; Miller, A. "Gold Code Generators in Virtex Devices" (PDF). Xilinx.com. Archived from the original (PDF) on July 5, 2008.**^**"Transmitted GPS Signals".*The GPS System*. kowoma.de. Archived from the original on 2012-08-04.**^**"Robert Gold, BS, MS, Ph.D." Robert Gold Comm Systems. 2011.**^**Gold, R. (October 1967). "Optimal binary sequences for spread spectrum multiplexing (Corresp.)".*IEEE Transactions on Information Theory*.**13**(4): 619–621. doi:10.1109/TIT.1967.1054048.**^**Holmes 2007, p. 100

## Further reading

- Holmes, Jack K. (30 June 2007).
*Spread Spectrum Systems for GNSS and Wireless Communications*. GNSS Technology and Applications Series.**45**. Artech House. ISBN 978-1-59693-083-4.

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