On MDS codes via Cauchy matrices

Abstract

A special form of Cauchy matrix is used to obtain a tighter bound for the validity region of the maximum distance separable (MDS) conjecture and a new compact characterization of generalized Reed-Solomon codes. The latter is further used to obtain constructions and some existence results for long (2k, k) double-circulant MDS codes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>