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 $P$.