# 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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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.