On the equivalence of the Berlekamp-Massey and the euclidean algorithms for algebraic decoding

Abstract

Dornstetter, Heydtmann, and Jensen have previously demonstrated that the Extended Euclidean algorithm and the Berlekamp-Massey algorithm are two equivalent methods used for solving the so-called Key Equation in BCH and Reed-Solomon decoding. This paper presents a new algorithm which makes this correspondence more explicit and is an improvement over each of the two algorithms.