BCH code
In coding theory, the BCH codes form a class of cyclic error-correcting codes that are constructed using finite fields. BCH codes were invented in 1959 by French mathematician Alexis Hocquenghem, and independently in 1960 by Raj Bose and D. K. Ray-Chaudhuri. The acronym BCH comprises the initials of these inventors' surnames (mistakenly, in the case of Ray-Chaudhuri).
One of the key features of BCH codes is that during code design, there is a precise control over the number of symbol errors correctable by the code. In particular, it is possible to design binary BCH codes that can correct multiple bit errors. Another advantage of BCH codes is the ease with which they can be decoded, namely, via an algebraic method known as syndrome decoding. This simplifies the design of the decoder for these codes, using small low-power electronic hardware.
BCH codes are used in applications such as satellite communications,compact disc players, DVDs, disk drives, solid-state drives and two-dimensional bar codes.
Given a prime power q and positive integers m and d with d ≤ qm − 1, a primitive narrow-sense BCH code over the finite field GF(q) with code length n = qm − 1 and distance at least d is constructed by the following method.
...
Wikipedia