Algebraic Structures of Constacyclic Codes Over Finite Chain Rings and Power Series Rings

Abstract

Let R be a chain ring with the maximal ideal $$\langle \gamma \rangle$$ . In this paper, we shall study $$(r_1+r_2\gamma )$$ -constacyclic codes of arbitrary length over R, where $$r_1, r_2$$ are units in R. We shall obtain the generators of these codes and their duals. Moreover, a minimal spanning set (and so a generator matrix) for a constacyclic code is obtained. We shall determine the minimum Hamming distance of a constacyclic code over the chain ring R. At last, we shall study some constacyclic codes over formal power series rings. The minimal spanning set for these codes are also established.