The Structure of Constacyclic Codes of Length 2p^s over Finite Chain Ring: Wateekorn Sriwirach, Chakkrid Klin-eam - Team, Support (Thai Journal of Mathematics, 2019)
Let R be a finite commutative chain ring with identity of characteristic p^a that has maximal ideal z. In this paper, we study λ-constacyclic codes of length 2p^s over the ring R, for any unit λ of R. If the unit λ is not a square, the rings R_λ=R[x]x^2p^s-λ is a local ring with maximal ideal x^2-r, z, where rR such that λ-r^p^s is not invertible. When there exists a unit λ_0 of R such that λ=λ^p^s_0, we prove that x^2-λ_0 is nilpotent with nilpotency index ap^s-(a-1)p^s-1. When λ=λ^p^s_0+zω, for some unit ω of R, we show that R_λ is also a chain ring with maximal ideals x^2-λ_0. Moreover, when λ=λ^p^s_0+z^2ω, it shown that R_λ is a chain ring with maximal ideals x^2-λ_0. Furthermore, the algebraic structure and dual of all λ-constacyclic codes are obtained.