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

The Berlekamp-Massey (1968, 1969) algorithm (BMA) and the Euclidean algorithm (EA) for decoding have been considered as two different algorithms for solving the same problem, namely, the one given by the key equation. We argue that they are essentially identical by showing how one can be adapted to perform the same arithmetic as the other. As a tool we use Feng and Tzeng's (1991) fundamental iterative algorithm that when adapted to the syndrome matrix is regarded as equivalent to the BMA.