On constacyclic codes over finite chain rings

Let R be an arbitrary commutative finite chain ring, γ   a generator of the maximal ideal and R×R× the multiplicative group of units of R  . For any w∈R×w∈R×, the structural properties and dual codes of (1+wγ)(1+wγ)-constacyclic codes of arbitrary length over R   are given. As corollaries, self-dual constacyclic codes over the finite chain ring F2m+uF2mF2m+uF2m (u2=0u2=0) and the Galois ring GR(2s,m)GR(2s,m) are provided.