Editing Gold code

{{Short description|Binary codes in telecommunications and GPS}}
{{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}}

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> &minus; 1.

A set of Gold codes can be generated with the following steps.  Pick two [[maximum length sequence]]s of the same length 2<sup>''n''</sup> &minus; 1 such that their absolute [[cross-correlation]] is less than or equal to 2<sup>(''n''+2)/2</sup>, where ''n'' is the size of the [[linear-feedback shift register]] used to generate the maximum length sequence (Gold '67).  The set of the 2<sup>''n''</sup> &minus; 1 [[exclusive-or]]s 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 2<sup>''n''</sup> + 1  Gold code sequences.  The highest absolute cross-correlation in this set of codes is 2<sup>(''n''+2)/2</sup> + 1 for even ''n'' and 2<sup>(''n''+1)/2</sup> + 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{{spaced ndash}}the number of ones and zeros differs by only one.<ref name="Holmes_2007"/>

Gold codes are used in [[GPS]]. The [[GPS signals#Coarse/acquisition code|GPS C/A]] ranging codes are Gold codes of period 1,023.

==See also==
*[[Hadamard code]]
*[[JPL code]]
*[[Kasami code]]
*[[Zadoff–Chu sequence]]
*[[Complementary sequences]]
*[[Space Network]] – a NASA system that uses Gold codes

==References==
{{reflist|refs=
<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="Gold_2011">{{cite web |title=Robert Gold, BS, MS, Ph.D. |date=2011 |publisher=Robert Gold Comm Systems |url=http://www.rgcsystems.com/ppl1_gold.htm |access-date=2008-07-18  |archive-date=2017-06-24  |archive-url=https://web.archive.org/web/20170624101852/http://www.rgcsystems.com/ppl1_gold.htm |url-status=dead }}</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>
}}

==Further reading==
* {{cite book |author-first=Alois M. J. |author-last=Goiser |title=Handbuch der Spread-Spectrum Technik |trans-title=Handbook of the spread-spectrum technique |language=de |publisher=[[Springer Verlag]] |publication-place=Vienna, Austria |date=1998 |edition=1 |isbn=3-211-83080-4 |chapter=4.3.2. Gold-Folgen |trans-chapter=Gold sequences}}
* {{cite book |title=Spread Spectrum in Communication |date=1985 |edition=1 |publisher=Peter Peregrinus Ltd. <!-- printer: Short Run Press Ltd., Exeter, UK --> / [[The Institution of Electrical Engineers]] |publication-place=London, UK |series=IEE Telecommunications Series |volume=12 |author-first1=Reidar |author-last1=Skaug |author-first2=Jens F. |author-last2=Hjelmstad |editor-first1=J. E. |editor-last1=Flood |editor-first2=C. J. |editor-last2=Hughes |isbn=0-86341-034-0 |pages=82– |chapter=Coding for bandwidth spreading}} (xii+201+1 pages)
* {{cite book |title=Modulationsverfahren |chapter=46.3.1 Gold-Codes |language=de |author-first1=Dietmar |author-last1=Rudolph |author-first2=Matthias |author-last2=Rudolph |date=2011-04-12 |publisher=[[Brandenburg University of Technology]] (BTU) |publication-place=Cottbus, Germany |pages=212–214 |url=http://www.diru-beze.de/modulationen/skripte/Modulationsverfahren.pdf |access-date=2021-06-14 |url-status=live |archive-url=https://web.archive.org/web/20210616042506/http://www.diru-beze.de/modulationen/skripte/Modulationsverfahren.pdf |archive-date=2021-06-16}} (xiv+225 pages)

{{CDMA}}

{{DEFAULTSORT:Gold Code}}
[[Category:Line codes]]

[[de:Linear rückgekoppeltes Schieberegister#Gold-Folgen]]