Editing Gold code (section)

{{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.