A New Procedure for Decoding Cyclic and Bch Codes Up to Actual Minimum Distance

In this paper, a new procedure for decoding cyclic and BCH codes up to their actual minimum distance is presented. Previous algebraic decoding procedures for cyclic and BCH codes such as the Peterson decoding procedure and our procedure using nonrecurrent syndrome dependence relations can be regarded as special cases of this new decoding procedure. With the aid of a computer program, it has been verified that, using this new decoding procedure, all binary cyclic and BCH codes of length 63 or less can be decoded up to their actual minimum distance. The procedure incorporates an extension of our Fundamental Iterative Algorithm and the complexity of this decoding procedure is O(n/sup 3/).