Dey, Bikash Kumar and Rajan, Sundar B (2004) Codes Closed under Arbitrary Abelian Group of Permutations. In: SIAM Journal on Discrete Mathematics, 18 (1). pp. 1-18.
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Abstract
Algebraic structure of codes over $F_{q}$, closed under arbitrary abelian group G of permutations with exponent relatively prime to q, called G-invariant codes, is investigated using a transform domain approach. In particular, this general approach unveils algebraic structure of quasicyclic codes, abelian codes, cyclic codes, and quasi-abelian codes with restriction on G to appropriate special cases. Dual codes of G-invariant codes and self-dual G-invariant codes are characterized. The number of G-invariant self-dual codes for any abelian group G is found. In particular, this gives the number of self-dual l-quasi-cyclic codes of length ml over $ F_{q}$ when (m, q) = 1. We extend Tanner’s approach for getting a bound on the minimum distance from a set of parity check equations over an extension field and outline how it can be used to get a minimum distance bound for a G-invariant code. Karlin’s decoding algorithm for a systematic quasi-cyclic code with a single row of circulants in the generator matrix is extended to the case of systematic quasi-abelian codes. In particular, this can be used to decode systematic quasi-cyclic codes with columns of parity circulants in the generator matrix.
Item Type: | Journal Article |
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Publication: | SIAM Journal on Discrete Mathematics |
Publisher: | Society for Industrial and Applied Mathematics (SIAM) |
Additional Information: | The copyright of this article belongs to Society for Industrial and Applied Mathematics (SIAM). |
Keywords: | quasi-cyclic codes;permutation group of codes;discrete Fourier transform;self-dual codes |
Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
Date Deposited: | 20 Nov 2007 |
Last Modified: | 19 Sep 2010 04:17 |
URI: | http://eprints.iisc.ac.in/id/eprint/2310 |
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