A Gold code, also known as Gold sequence, is a type of binary

sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called ...

, used in

telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that ...

( CDMA) and satellite navigation ( GPS). Gold codes are named after Robert Gold. Gold codes have bounded small

cross-correlation In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a ''sliding dot product'' or ''sliding inner-product''. It is commonly used f ...

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^''n'' + 1 sequences each one with a period of 2^''n'' − 1. A set of Gold codes can be generated with the following steps. Pick two maximum length sequences of the same length 2^''n'' − 1 such that their absolute

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 (Gold '67). The set of the 2^''n'' − 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 2^''n'' + 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 Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , ...

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 balancedthe number of ones and zeros differs by only one. Gold codes are used in GPS. The GPS C/A ranging codes are Gold codes of period 1,023.

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Further reading