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Consta-Abelian Codes Over Galois Rings

Kiran, T and Rajan, Sundar B (2004) Consta-Abelian Codes Over Galois Rings. In: IEEE Transactions on Information Theory, 50 (2). pp. 367-380.


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We study $n-length$ consta-Abelian codes (a generalization of the well-known Abelian codes and constacyclic codes) over Galois rings of characteristic $p^a$, where $n$ and $p$ are coprime. A twisted discrete Fourier transform (DFT) is used to generalize transform domain results of Abelian and constacyclic codes, to consta-Abelian codes. Further, we characterize consta-Abelian codes invariant under two kinds of monomials, whose underlying permutations are effected by: i) multiplying the coordinates with a unit in the appropriate mixed-radix representation of the coordinate positions and ii) shifting the coordinates by $t$ positions. All the codes studied here belong to the class of quasi-twisted codes which are known to contain some good codes. We show that the dual of a consta-Abelian code invariant under the two monomials is also a consta-Abelian code closed under both monomials.

Item Type: Journal Article
Publication: IEEE Transactions on Information Theory
Publisher: IEEE
Additional Information: �©1990 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: Abelian codes;Consta-Abelian codes;Constacyclic codes; Galois rings;Quasi-twisted (QT) codes;Twisted discrete fourier transform
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 30 Nov 2005
Last Modified: 19 Sep 2010 04:21
URI: http://eprints.iisc.ac.in/id/eprint/4223

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