Double Constacyclic Codes Over Two Finite Commutative Chain Rings

Many kinds of codes which possess two cycle structures over special finite commutative chain rings, such as ${\mathbb {Z}}_{2}{\mathbb {Z}}_{4}$ -additive cyclic and quasi-cyclic fractional index etc., were proved asymptotically good. In this paper we extend the study in directions: consider any rings with a surjective homomorphism from one to other, double constacyclic structures. We construct an extensive kind rings. And, developing probabilistic method suitable for fields, prove that are