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# Gold code

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 Title: Gold code Author: World Heritage Encyclopedia Language: English Subject: Collection: Line Codes Publisher: World Heritage Encyclopedia Publication Date:

### Gold code

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] 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 LFSR 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) is a set of Gold codes. 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.[4]

## References

Inline references
1. ^ George, M.; Hamid, M.; Miller, A. "Gold Code Generators in Virtex Devices" (PDF). Xilinx.com.
2. ^ "Transmitted GPS Signals". The GPS System. kowoma.de.
3. ^ "Robert Gold, BS, MS, Ph.D.". Robert Gold Comm Systems. 2011.
4. ^ Holmes 2007, p. 100
General references
• Gold, R. (October 1967). "Optimal binary sequences for spread spectrum multiplexing (Corresp.)". IEEE Transactions on Information Theory 13 (4): 619–621.
• Holmes, Jack K. (30 June 2007). Spread Spectrum Systems for GNSS and Wireless Communications. GNSS Technology and Applications Series 45. Artech House.
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