# Matrix Characterization of Generalized Hamming Weights

Viswanath, G and Rajan, Sundar B (2001) Matrix Characterization of Generalized Hamming Weights. In: 2001 IEEE International Symposium on Information Theory, 24-29 June, Washington, p. 61.

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## Abstract

A linear code with the systematic generator matrix [I|P] is maximum distance separable (MDS) if and only if every square submatrix of P is nonsingular. We obtain similar matrix characterization for all linear codes with a specified Hamming weight hierarchy (HWH). Using this we characterize near-MDS codes (NMDS), near-near-MDS $(N^2MDS)$ codes and a generalization of these codes called $N^{\mu}MDS$ codes in terms of their systematic generator matrices.

Item Type: Conference Paper Copyright 1990 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Division of Electrical Sciences > Electrical Communication Engineering 15 Feb 2006 01 Jul 2011 07:13 http://eprints.iisc.ernet.in/id/eprint/5365