Algebraic Decoding of the (31, 16, 7) Quadratic Residue Code by Using Berlekamp-Massey Algorithm

An algebraic decoding of the (89, 45, 17) quadratic residue code suggested by Truong et al. (2008) has been designed that uses the inverse-free Berlekamp-Massey (BM) algorithm to determine the error-locator polynomial and applies a verification method to check whether the error pattern obtained by decoding algorithm is correct or not. In this paper, based on the ideas of the algorithm mentioned above, two decoding methods of the (31, 16, 7) binary quadratic residue code are proposed. Also, the comparison of the decoding complexity in terms of CPU time of these two methods and the conventional algebraic decoding method proposed by Reed et al. (1990) are given.