Algebraic Decoding of the Quadratic Residue Code

ArticleinIEEE Transactions on Information Theory 54(11):5005-5011 · November 2008with2 Reads
Impact Factor: 2.33 · DOI: 10.1109/TIT.2008.929956 · Source: DBLP


    Recently, an algebraic decoding algorithm suggested by Truong (2005) for some quadratic residue codes with irreducible generating polynomials has been designed that uses the inverse-free Berlekamp-Massey (BM) algorithm to determine the error-locator polynomial. In this paper, based on the ideas of the algorithm mentioned above, an algebraic decoder for the (89, 45, 17) binary quadratic residue code, the last one not decoded yet of length less than 100 , is proposed. It was also verified theoretically for all error patterns within the error-correcting capacity of the code. Moreover, the verification method developed in this paper can be extended for all cyclic codes without checking all error patterns by computer simulations.