Decoding cyclic and BCH codes up to actual minimum distance using nonrecurrent syndrome dependence relations

The decoding capabilities of algebraic algorithms, mainly the Berlekamp-Massey algorithm, the Euclidean algorithm, and the authors´ (1989) generalizations of these algorithms, are basically constrained by the minimum distance bounds of the codes. The authors introduce a more general procedure which breaks away from this restriction and which can determine the, error locations from nonrecurrent dependence relations among the syndromes. It can decode many cyclic and BCH codes up to their actual minimum distance and is seen to be a generalization of the procedure introduced by W.W. Peterson and E.J. Weldon (1972)