Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Gold code
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
{{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> − 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> − 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> − 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]]
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)
Pages transcluded onto the current version of this page
(
help
)
:
Template:About
(
edit
)
Template:CDMA
(
edit
)
Template:Cite book
(
edit
)
Template:Reflist
(
edit
)
Template:Short description
(
edit
)
Template:Spaced ndash
(
edit
)
Template:Use dmy dates
(
edit
)