Self-dual cyclic codes over finite chain rings

Bocong Chen; San Ling; Guanghui Zhang

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arXiv · 1405.2602

Self-dual cyclic codes over finite chain rings

Bocong Chen·San Ling·Guanghui Zhang

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Abstract

Let $R$ be a finite commutative chain ring with unique maximal ideal $\langle \gamma\rangle$, and let $n$ be a positive integer coprime with the characteristic of $R/\langle \gamma\rangle$. In this paper, the algebraic structure of cyclic codes of length $n$ over $R$ is investigated. Some new necessary and sufficient conditions for the existence of nontrivial self-dual cyclic codes are provided. An enumeration formula for the self-dual cyclic codes is also studied.

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Bocong Chen, San Ling, Guanghui Zhang. 2014-05-11. Self-dual cyclic codes over finite chain rings. https://arxiv.org/abs/1405.2602

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