Self-Dual Abelian Codes in Some Nonprincipal Ideal Group Algebras

Parinyawat Choosuwan, Somphong Jitman and Patanee Udomkavanich

Mathematical Problems in Engineering, 2016, vol. 2016, 1-12

Abstract:

The main focus of this paper is the complete enumeration of self-dual abelian codes in nonprincipal ideal group algebras with respect to both the Euclidean and Hermitian inner products, where and are positive integers and is an abelian group of odd order. Based on the well-known characterization of Euclidean and Hermitian self-dual abelian codes, we show that such enumeration can be obtained in terms of a suitable product of the number of cyclic codes, the number of Euclidean self-dual cyclic codes, and the number of Hermitian self-dual cyclic codes of length over some Galois extensions of the ring , where . Subsequently, general results on the characterization and enumeration of cyclic codes and self-dual codes of length over are given. Combining these results, the complete enumeration of self-dual abelian codes in is therefore obtained.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:9020173

DOI: 10.1155/2016/9020173

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