A Generalized Rational Interpolation Problem and the Solution of the Welch–Berlekamp Key Equation

We show that an algorithm designed to solve the Welch–Berlekamp key equation may also be used to solve a more general problem, which can be regarded as a finite analogue of a generalized rational interpolation problem. As a consequence, we show that a single algorithm exists which can solve both Berlekamp's classical key equation (usually solved by the Berlekamp–Massey algorithm) and the Welch–Berlekamp key equation which arise in the decoding of Reed–Solomon codes.