Algorithms for decoding and interpolation

Abstract

In this paper we consider various algorithms for decoding BCH/RS/ Goppa codes, in particular the euclidean algorithm, the Beriekamp-Massey algorithm and the Welch-Beriekamp algorithm. We focus on relationships of these algorithms with interpolation methods in system theory. We note that the problem statements in the two areas can be different: from a system theoretic point of view, rational interpolating functions with common factors between numerator and denominator are undesirable whereas common factors can be required in a decoding context.The behavioral approach was introduced by Jan C. Willems into system theory in the eighties. It proposes the family of trajectories of a system as its ..