Galois ring codes and their images under various bases

Abstract

In this paper we consider linear block codes B of length n over the Galois ring GR(pr, m) and obtain their images with respect to various bases of GR(pr, m) seen as a free module of rank m over the residue class ring ℤpr. Interesting new examples of dual, normal and self-dual bases of GR(pr, m) and their relationships are given. The image of B is a linear block code over ℤpr of length mn and its generator matrix is formed row-wise by the images of βiG, where is a chosen basis of GR(pr, m) and G is a generator matrix of B. Certain conditions in which the pr-ary image is distance-invariant after a change in basis are investigated. Consequently a new quaternary code endowed with a homogeneous metric that is optimal with respect to certain known bounds is constructed.