# Gold code

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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 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 (Gold '67). 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 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.

## References

1. ^ George, Maria; Hamid, Mujtaba; Miller, Andy (2001-01-10). "Gold Code Generators in Virtex Devices" (PDF). Virtex Series, Virtex-II Series, and Spartan-II family (Application note). 1.1. Xilinx. XAPP217. Archived from the original (PDF) on 2008-07-05. (9 pages)
2. ^ "Transmitted GPS Signals". The GPS System. kowoma GPS. 2009-04-19. Archived from the original on 2012-08-04.
3. ^ "Robert Gold, BS, MS, Ph.D." Robert Gold Comm Systems. 2011.
4. ^ Gold, Robert (October 1967). "Optimal binary sequences for spread spectrum multiplexing". IEEE Transactions on Information Theory (Correspondence). IT-13 (4): 619–621. doi:10.1109/TIT.1967.1054048.
5. ^ Holmes, Jack K. (2007-06-30). Spread Spectrum Systems for GNSS and Wireless Communications. GNSS Technology and Applications Series. 45. Artech House. p. 100. ISBN 978-1-59693-083-4.

## Further reading

• Goiser, Alois M. J. (1998). "4.3.2. Gold-Folgen" [Gold sequences]. Handbuch der Spread-Spectrum Technik [Handbook of the spread-spectrum technique] (in German) (1 ed.). Vienna, Austria: Springer Verlag. ISBN 3-211-83080-4.
• Skaug, Reidar; Hjelmstad, Jens F. (1985). "Coding for bandwidth spreading". In Flood, J. E.; Hughes, C. J. (eds.). Spread Spectrum in Communication. IEE Telecommunications Series. 12 (1 ed.). London, UK: Peter Peregrinus Ltd. / The Institution of Electrical Engineers. pp. 82–. ISBN 0-86341-034-0. (xii+201+1 pages)
• Rudolph, Dietmar; Rudolph, Matthias (2011-04-12). "46.3.1 Gold-Codes". Modulationsverfahren (PDF) (in German). Cottbus, Germany: Brandenburg University of Technology (BTU). pp. 212–214. Archived (PDF) from the original on 2021-06-16. Retrieved 2021-06-14. (xiv+225 pages)