Enumeration formulas for self-dual cyclic codes

Let R   be a finite commutative chain ring with unique maximal ideal 〈γ〉〈γ〉, and let n   be a positive integer relatively prime to the characteristic of R/〈γ〉R/〈γ〉. In this paper, some new necessary and sufficient conditions for the existence of nontrivial self-dual cyclic codes of length n over R are provided. Explicit enumeration formulas for self-dual cyclic codes over R are studied. In particular, several main results of [21] are special cases of the present paper.