Title :
Matrix characterization of generalized Hamming weights
Author :
Viswanath, G. ; Rajan, B. Sundar
Author_Institution :
Dept. of Electr. Commun. Eng., Indian Inst. of Sci., Bangalore, India
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 (N2MDS) codes and a generalization of these codes called NμMDS codes in terms of their systematic generator matrices
Keywords :
linear codes; matrix algebra; Hamming weight hierarchy; NμMDS codes; N2MDS codes; NMDS; generalized Hamming weights; linear code; matrix characterization; maximum distance separable code; near-MDS codes; near-near-MDS codes; nonsingular square submatrix; systematic generator matrix; Character generation; Hamming weight; Linear code; Parity check codes;
Conference_Titel :
Information Theory, 2001. Proceedings. 2001 IEEE International Symposium on
Conference_Location :
Washington, DC
Print_ISBN :
0-7803-7123-2
DOI :
10.1109/ISIT.2001.935924
