On trace codes and Galois invariance over finite commutative chain rings

Codes over finite commutative chain rings have been introduced as a generalization of codes over finite fields. Let S|RS|R be a Galois extension of finite commutative chain rings. If C⊆SnC⊆Sn is an S-code, it is possible to define, starting from C, two different R  -codes: Res(C)=C∩RnRes(C)=C∩Rn and Tr(C)Tr(C), where Tr is the trace function. In this work we analyze the relationships between these R-codes and the duality operator.