Galois correspondence on linear codes over finite chain rings

Abstract

Let S|T be a Galois extension of finite chain rings and consider H as its group of ring-automorphisms fixing the elements in T. In this paper we determine the stabilizer under such a group of any S-linear code. Using the so called Galois interior a correspondence between subgroups of H and a set of S-linear subcodes of B is determined. Some improvements of upper and lower bounds for the rank of the Galois-subring subcode and trace code are derived from this construction.