Gold code: Difference between revisions
imported>GhostInTheMachine explain why they are used |
imported>GhostInTheMachine Changing short description from "A type of binary sequence used in telecommunications" to "Binary sequence used in telecommunications" |
||
| Line 1: | Line 1: | ||
{{Short description|Binary | {{Short description|Binary sequence 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}} | {{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]] | 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.<ref name="Gold_1967"/> 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''. | 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.<ref name="Gold_1967"/> 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''. | ||
Latest revision as of 08:24, 17 April 2026
Template:Short description Script error: No such module "Unsubst". Script error: No such module "about". Script error: No such module "Unsubst".
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
- Script error: No such module "citation/CS1".
- Script error: No such module "citation/CS1". (xii+201+1 pages)
- Script error: No such module "citation/CS1". (xiv+225 pages)
Script error: No such module "Navbox".