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

Authors:
Simon R. Blackburn
Affiliations:
Information Security Group, Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom.
Venue:
Designs, Codes and Cryptography
Year:
1997

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Abstract

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