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 ...Show MoreMetadata
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/sup 2/MDS) codes and a generalization of these codes called N/sup /spl mu//MDS codes in terms of their systematic generator matrices.
Published in: Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252)
Date of Conference: 29-29 June 2001
Date Added to IEEE Xplore: 07 August 2002
Print ISBN:0-7803-7123-2
Contents 