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Matrix characterization of generalized Hamming weights

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2 Author(s)
Viswanath, G. ; Dept. of Electr. Commun. Eng., Indian Inst. of Sci., Bangalore, India ; Rajan, B.S.

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 (N2MDS) codes and a generalization of these codes called NμMDS codes in terms of their systematic generator matrices

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Information Theory, 2001. Proceedings. 2001 IEEE International Symposium on

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