Gold code 50567 222176527 2008-06-27T22:53:27Z Alaibot 1324179 Robot: Changing template: com-stub :''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>&nbsp;+&nbsp;1 sequences each one with a period of 2<sup>''m''</sub>&nbsp;−&nbsp;1. All 2<sup>''m''</sub>&nbsp;+&nbsp;1 sequences are balanced and contain either 2<sup>''m''−1</sub> ones and 2<sup>''m''−1</sub>&nbsp;−&nbsp;1 zeros or 2<sup>''m''−1</sub>&nbsp;−&nbsp;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]] {{telecomm-stub}} [[de:Linear rückgekoppeltes Schieberegister#Gold-Folgen]] [[ru:Коды Голда]]