Gold code: Difference between revisions
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{{Short description|Binary codes in telecommunications | {{Short description|Binary codes used in telecommunications}} | ||
{{Use dmy dates|date=January 2021|cs1-dates=y}} | {{Use dmy dates|date=January 2021|cs1-dates=y}} | ||
{{About|binary codes used in radiocommunications|the authentication codes used to command a launch of nuclear weapons|Gold Codes}} | {{About|binary codes used in radiocommunications|the authentication codes used to command a launch of nuclear weapons|Gold Codes}} | ||
{{Confusing|date=December 2025|reason=why are these codes used? What advantage do they offer? Maybe add some form of example of a set of codes}} | |||
A '''Gold code''', also known as '''Gold sequence''', is a type of binary [[sequence]], used in [[telecommunications]] ([[CDMA]])<ref name="George-Hamid-Miller_2008"/> and satellite navigation ([[GPS]]).<ref name="GPS_2009"/> Gold codes are named after Robert Gold.<ref name="Gold_2011"/><ref name="Gold_1967"/> Gold codes have bounded small [[cross-correlation]]s 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<sup>''n''</sup> + 1 sequences each one with a period of 2<sup>''n''</sup> − 1. | A '''Gold code''', also known as '''Gold sequence''', is a type of binary [[sequence]], used in [[telecommunications]] ([[CDMA]])<ref name="George-Hamid-Miller_2008"/> and satellite navigation ([[GPS]]).<ref name="GPS_2009"/> Gold codes are named after Robert Gold.<ref name="Gold_2011"/><ref name="Gold_1967"/> Gold codes have bounded small [[cross-correlation]]s 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<sup>''n''</sup> + 1 sequences each one with a period of 2<sup>''n''</sup> − 1. | ||
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==See also== | ==See also== | ||
*[[Hadamard code]] | *[[Hadamard code]] | ||
*[[Hamming code]] | |||
*[[JPL code]] | *[[JPL code]] | ||
*[[Kasami code]] | *[[Kasami code]] | ||
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==References== | ==References== | ||
<references> | |||
<ref name="George-Hamid-Miller_2008">{{cite web |last1=George |first1=Maria |last2=Hamid |first2=Mujtaba |last3=Miller |first3=Andy |title=Gold Code Generators in Virtex Devices |type=Application note |publisher=[[Xilinx]] |id=XAPP217 |version=1.1 |work=Virtex Series, Virtex-II Series, and Spartan-II family |date=2001-01-10 |url=http://www.xilinx.com/support/documentation/application_notes/xapp217.pdf |url-status=dead |archive-url=https://web.archive.org/web/20080705134550/http://www.xilinx.com/support/documentation/application_notes/xapp217.pdf |archive-date=2008-07-05}} (9 pages)</ref> | <ref name="George-Hamid-Miller_2008">{{cite web |last1=George |first1=Maria |last2=Hamid |first2=Mujtaba |last3=Miller |first3=Andy |title=Gold Code Generators in Virtex Devices |type=Application note |publisher=[[Xilinx]] |id=XAPP217 |version=1.1 |work=Virtex Series, Virtex-II Series, and Spartan-II family |date=2001-01-10 |url=http://www.xilinx.com/support/documentation/application_notes/xapp217.pdf |url-status=dead |archive-url=https://web.archive.org/web/20080705134550/http://www.xilinx.com/support/documentation/application_notes/xapp217.pdf |archive-date=2008-07-05}} (9 pages)</ref> | ||
<ref name="GPS_2009">{{cite web |title=Transmitted GPS Signals |date=2009-04-19 |work=The GPS System |publisher=kowoma GPS |url=http://www.kowoma.de/en/gps/signals.htm |archive-url=https://archive.today/20120804185510/http://www.kowoma.de/en/gps/signals.htm |url-status=dead |archive-date=2012-08-04}}</ref> | <ref name="GPS_2009">{{cite web |title=Transmitted GPS Signals |date=2009-04-19 |work=The GPS System |publisher=kowoma GPS |url=http://www.kowoma.de/en/gps/signals.htm |archive-url=https://archive.today/20120804185510/http://www.kowoma.de/en/gps/signals.htm |url-status=dead |archive-date=2012-08-04}}</ref> | ||
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<ref name="Gold_1967">{{cite journal |author-last=Gold |author-first=Robert |title=Optimal binary sequences for spread spectrum multiplexing |type=Correspondence |journal=[[IEEE Transactions on Information Theory]] |volume=IT-13 |issue=4 |pages=619–621 |date=October 1967 |doi=10.1109/TIT.1967.1054048}}</ref> | <ref name="Gold_1967">{{cite journal |author-last=Gold |author-first=Robert |title=Optimal binary sequences for spread spectrum multiplexing |type=Correspondence |journal=[[IEEE Transactions on Information Theory]] |volume=IT-13 |issue=4 |pages=619–621 |date=October 1967 |doi=10.1109/TIT.1967.1054048}}</ref> | ||
<ref name="Holmes_2007">{{cite book |first=Jack K. |last=Holmes |title=Spread Spectrum Systems for GNSS and Wireless Communications |url=https://books.google.com/books?id=-AUfAQAAIAAJ |date=2007-06-30 |publisher=Artech House |isbn=978-1-59693-083-4 |volume=45 |series=GNSS Technology and Applications Series |page=100}}</ref> | <ref name="Holmes_2007">{{cite book |first=Jack K. |last=Holmes |title=Spread Spectrum Systems for GNSS and Wireless Communications |url=https://books.google.com/books?id=-AUfAQAAIAAJ |date=2007-06-30 |publisher=Artech House |isbn=978-1-59693-083-4 |volume=45 |series=GNSS Technology and Applications Series |page=100}}</ref> | ||
</references> | |||
==Further reading== | ==Further reading== | ||
Latest revision as of 22:49, 31 December 2025
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A Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunications (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.[4] 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 balancedTemplate:Spaced ndashthe 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
- Hadamard code
- Hamming code
- JPL code
- Kasami code
- Zadoff–Chu sequence
- Complementary sequences
- Space Network – a NASA system that uses Gold codes
References
Further reading
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