Algebraic decoding of (71,36,11) quadratic residue code using Berlekamp-Massey algorithm

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 He et al. [2001], one can express unknown syndromes as functions of known syndromes. Unknown syndromes are determined by an efficient algorithm also developed in this paper. With the experience of unknown syndromes, one obtains the consecutive syndromes that are needed for the application of the inverse-free BM algorithm. The new decoding scheme, developed here can be used to implement the (71,36,11) QR code which has not been treated so far. It is verified by a computer program that uses the C++ language.