A simple decoding of BCH codes over GF(2m)

A simple decoding method for even minimum-distance Bose-Chaudhuri-Hochquenghem (BCH) codes is proposed. In the method the coefficients of an error locator polynomial are given as simple determinants (named Q determinants) composed of syndromes. The error evaluator is realized as a Q determinant divided by an error locator polynomial. The Q determinants can be efficiently obtained with very simple calculations on syndromes enabling the realization of a high-speed decoder of simple configuration. The number of calculations in obtaining the error locator and the error evaluator with the proposed method is smaller than that with the widely used Berlekamp-Massey algorithm when the number of correctable errors of the code is five or less. The proposed method can also be applied to the binary narrow-sense BCH codes of odd minimum distance