Comparison of Two Algorithms for Decoding Alternant Codes

Abstract

We compare the key equation solving algorithm introduced by Fitzpatrick to the Berlekamp-Massey algorithm. Our main result is that the two algorithms have the same computational complexity. It follows that in practice Fitzpatricks algorithm improves on Berlekamp-Massey since it uses less storage and has a simpler control structure. We also give an improved version of Fitzpatricks algorithm and a new simplified proof of the central inductive step in the argument.