Codes closed under arbitrary abelian group of permutations

Dey, Bikash Kumar ; Sundar Rajan, B. (2004) Codes closed under arbitrary abelian group of permutations SIAM Journal on Discrete Mathematics, 18 (1). pp. 1-18. ISSN 0895-4801

Full text not available from this repository.

Official URL:

Related URL:


Algebraic structure of codes over Fq, 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 quasi-cyclic 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 Fq 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:Article
Source:Copyright of this article belongs to Society for Industrial and Applied Mathematics.
Keywords:Quasi-Cyclic Codes; Permutation Group of Codes; Discrete Fourier Transform; Self-Dual Codes
ID Code:108066
Deposited On:08 Dec 2017 10:15
Last Modified:08 Dec 2017 10:15

Repository Staff Only: item control page