BCH code: Difference between revisions

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A '''BCH (Bose, Ray-Chaudhuri, Hocquenghem) code''' is a much studied ''code'' within the study of [[coding theory]] and more specifiically error-correcting codes. Roughly, a code is a way of encoding information to be transmitted so that any error introduced (e.g. by noise) during the transmission may be corrected on the receiving end. In technical terms it is multilevel, cyclic, [[error]]-correcting, variable-length [[digital]] [[code]] used to correct mutiple random error patterns. BCH codes may also be used with multilevel [[phase-shift keying]] whenever the number of levels is a prime number or a power of a [[prime number]]. A BCH code in 11 levels has been used to represent the 10 decimal digits plus a sign [[numerical digit|digit]].

== Construction ==

BCH codes are not limited to [[Binary Code|binary]] codes, but may be used with multilevel [[phase-shift keying]] whenever the number of levels is a prime number or a power of a [[prime number]]. A BCH code in 11 levels has been used to represent the 10 decimal digits plus a sign [[numerical digit|digit]].

BCH codes make use of [[field theory (mathematics)|field theory]] and polynomials over thatfinite fieldfields. TheTo waydetect theerrors a check polynomial iscan be constructed providesso the keyreceiving end tocan indicatingdetect thatif ansome errorerrors hashad occurred.

BCH codes make use of [[field theory (mathematics)|field theory]] and polynomials over that field. The way the check polynomial is constructed provides the key to indicating that an error has occurred.

If we wish to construct a BCH code to detect and correct 2 errors we use the [[finite field]] GF(16) or '''Z'''₂[''x'']/<''x''⁴+''x''+1>