Generation of matrices for determining minimum distance and decoding of cyclic codes

A simple method based on Newton´s identities and their extensions is presented for determining the actual minimum distance of cyclic codes. The method is also shown to be capable of producing results from the shifting method of van Lint and Wilson (1986). More significantly, it is shown that this method also provides a mechanism for generating the type of syndrome matrices needed by Feng-Tzeng´s algorithm for decoding cyclic and BCH codes up to their actual minimum distance