A Matrix Characterization of \(Near – MDS\) codes

Abstract

It is well known that a linear code over a finite field with the systematic generator matrix \([I | P]\) is MDS (Maximum Distance Separable) if and only if every square submatrix of \(P\) is nonsingular. In this correspondence, we obtain a similar characterization for the class of Near-MDS codes in terms of the submatrices of \(P\).