On trace codes and Galois invariance over finite commutative chain rings

摘要

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