Gold code
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2008-06-27T22:53:27Z
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:''This article is about binary codes used in telecommunications ([[CDMA]]) 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 sequence]]s, used in [[telecommunication]] ([[CDMA]])<ref>"[George, M., Hamid, M., and Miller A. {{PDFlink|[http://www.xilinx.com/support/documentation/application_notes/xapp217.pdf Gold Code Generators in Virtex Devices]}}</ref> and satellite navigation ([[GPS]])<ref>"[http://www.kowoma.de/en/gps/signals.htm GPS - explained (Signals)]"</ref>.
Pick two [[Maximum length sequence|''m''-sequences]] of the same length ''n'', such that their [[cross-correlation]] takes just three values. The set of the ''n'' [[exclusive-or]]s 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<sup>''m''</sub> + 1 sequences each one with a period of 2<sup>''m''</sub> − 1.
All 2<sup>''m''</sub> + 1 sequences are balanced and contain either 2<sup>''m''−1</sub> ones and 2<sup>''m''−1</sub> − 1 zeros or 2<sup>''m''−1</sub> − 1 ones and 2<sup>''m''−1</sub> zeros.
==References==
<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]]
[[category:Line codes]]
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[[de:Linear rückgekoppeltes Schieberegister#Gold-Folgen]]
[[ru:Коды Голда]]