Algorithm for solving the Welch-Berlekamp key-equation, with a simplified proof

An alternative technique due to Welch and Berlekamp (1983) for decoding Reed-Solomon codes has a key equation different in form from the key equation solved by the conventional Berlekamp-Massey algorithm or by the so-called Euclidean algorithm. The authors present an algorithm for solving the key equation which has a simple structure and which is readily shown to work.