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 calle ...

, 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 fe ...

(

CDMA Code-division multiple access (CDMA) is a channel access method used by various radio communication technologies. CDMA is an example of multiple access, where several transmitters can send information simultaneously over a single communicatio ...

) and satellite navigation (

GPS The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...

). Gold codes are named after Robert Gold. 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 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 sequence A maximum length sequence (MLS) is a type of pseudorandom binary sequence. They are bit sequences generated using maximal linear-feedback shift registers and are so called because they are periodic and reproduce every binary sequence (except th ...

s of the same length 2^''n'' − 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 In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function of single bits is exclusive-or (XOR). Thus, an LFSR is most often a ...

used to generate the maximum length sequence (Gold '67). The set of the 2^''n'' − 1

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, , , ...

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^''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

. The GPS C/A ranging codes are Gold codes of period 1,023.

See also

References

Further reading