Constacyclic Codes over Finite Chain Rings of Characteristic p

Let R be a finite commutative chain ring of characteristic p with invariants p,r, and k. In this paper, we study lambda-constacyclic codes of an arbitrary length N over R, where lambda is a unit of R. We first reduce this to investigate constacyclic codes of length ps (N=n1ps, p does not divide n1) over a certain finite chain ring CR(uk,rb) of characteristic p, which is an extension of R. Then we use discrete Fourier transform (DFT) to construct an isomorphism gamma between R[x]/ and a direct sum & OPLUS;b & ISIN;IS(rb) of certain local rings, where I is the complete set of representatives of p-cyclotomic cosets modulo n1. By this isomorphism, all codes over R and their dual codes are obtained from the ideals of S(rb). In addition, we determine explicitly the inverse of gamma so that the unique polynomial representations of lambda-constacyclic codes may be calculated. Finally, for k=2 the exact number of such codes is provided.