BCH codes

Abstract

Bose–Chaudhuri–Hocquenghem (BCH) codes are of great practical importance for error correction, particularly if the expected number of errors is small compared with the length. BCH codes were constructed as a generalization of Hamming codes. BCH codes are best considered as cyclic codes. A BCH code over GF(q) of length n and designed distance δ is the largest possible cyclic code having zeros where α E GF(qm) is a primitive nth root of unity, b is a nonnegative integer, and m is the multiplicative order of q modulo n. Important special cases are b = 1 (called narrow-sense BCH codes), or n = qm – l (called primitiue BCH codes). A BCH code is assumed to be narrow-sense and primitive unless stated otherwise. BCH codes with n = q – 1 (that is, m = 1, α ∈ GF(q)) are another important subclass. These are known as Reed–Solomon codes. © 1977, North-Holland Publishing Company