Euclidean Decoders for BCH Codes
Willard L. Eastman · 1988
Abstract : This report investigates conventional decoding algorithms for BCH codes. The algorithm of Sugiyama, Kasahara, Hirasawa and Namekawa, Mills' continued fraction algorithm, and the Berlekamp-Massey algorithm are all viewed as slightly differing variants of Euclid's algorithm. An improved version of Euclid's algorithm for polynomials is developed. The Berlekamp-Massey algorithm is extended within the Euclidean framework to avoid computation of vector inner products. Inversionless forms of the algorithms are considered and the results are extended to provide for decoding of erasures as well as errors. Keywords: Bose Chaudhuri Hocquenghem code; Very large scale integration; Two dimensional systolic arrays; Communications; Coding; Error correction codes.