Fast algorithm for computing the roots of error locator polynomials up to degree 11 in Reed-Solomon decoders

Abstract

The central problem in the implementation of a Reed-Solomon code is finding the roots of the error locator polynomial. In 1967, Berlekamp et al. found an algorithm for finding the roots of an affine polynomial in GF(2/sup m/) that can be used to solve this problem. In this paper, it is shown that this Berlekamp-Rumsey-Solomon (1967) algorithm, together with the Chien (1964) search method, makes possible a fast decoding algorithm in the standard-basis representation that is naturally suitable in a software implementation. Finally, simulation results for this fast algorithm are given.