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Self-dual cyclic codes over finite chain rings
Bocong Chen, San Ling, Guanghui Zhang · 2014-05-12 · via cs.IT updates on arXiv.org

Let $R$ be a finite commutative chain ring with unique maximal ideal $\langle γ\rangle$, and let $n$ be a positive integer coprime with the characteristic of $R/\langle γ\rangle$. 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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