On the equivalence of the Berlekamp-Massey and the Euclidean algorithms for decoding

The Berlekamp-Massey algorithm (BMA) and the Euclidean algorithm (EA) for d ecoding have been considered as two different algorithms for solving the sa me problem, namely, the one given by the key equation. In this corresponden ce we argue that they are essentially identical by showing how one can be a dapted to perform the same arithmetics as the other. As a tool we use Feng and Tzeng's Fundamental Iterative algorithm that when adapted to the syndro me matrix is regarded as equivalent to the BMA.