Algebraic decoding of (79,40,15) quadratic residue code using inverse-free Berlekamp-Massey algorithm

Abstract

In this paper, an algebraic decoding method is proposed for the quadratic residue codes that utilize the Berlekamp-Massey (BM) algorithm. By applying a technique developed in [l], one can express unknown syndromes as functions of known syndromes. The unknown syndromes are determined by an efficient algorithm also developed in this paper. With the appearance of unknown syndromes, one obtains the consecutive syndromes that are needed for the application of the inverse-free BM algorithm [2-51. The new decoding scheme developed here can be used to implement the (79, 40, 15) quadratic residue (QR) code which has not been treated so far. It is verified by a computer program that uses the C++ language.