  Many kinds of codes which possess two cycle structures over two special
finite commutative chain rings, such as ${\Bbb Z}_2{\Bbb Z}_4$-additive cyclic
codes and quasi-cyclic codes of fractional index etc., were proved
asymptotically good. In this paper we extend the study in two directions: we
consider any two finite commutative chain rings with a surjective homomorphism
from one to the other, and consider double constacyclic structures. We
construct an extensive kind of double constacyclic codes over two finite
commutative chain rings. And, developing a probabilistic method suitable for
quasi-cyclic codes over fields, we prove that the double constacyclic codes
over two finite commutative chain rings are asymptotically good.
