The Structure of Constacyclic Codes of Length 2ps over Finite Chain Rings

Let R be a finite commutative chain ring with identity of characteristic p(a) that has maximal ideal < z >. In this paper, we study lambda-constacyclic codes of length 2p(s) over R, for any unit lambda of R. If the unit lambda is not a square, the rings R-lambda = R[x]/< x(2)p(s) - lambda > is a local ring with maximal ideal < x(2) - r, z >, where r is an element of R such that lambda - r(ps) is not invertible. When there exists a unit lambda(0) of R such that lambda = lambda(ps)(0), we prove that x(2) - lambda(0) is nilpotent with nilpotency index ap(s) - (a - 1) p(s-1). When lambda = lambda(ps)(0) + zw, for some unit omega of R, we show that R-lambda is also a chain ring with maximal ideals < x(2) - lambda(0)>. Furthermore, the algebraic structure and dual of all lambda-constacyclic codes are obtained.