Self-dual cyclic codes over finite chain rings

Abstract

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

15 pages