Galois ring codes and their images under various bases

Abstract

© Published under licence by IOP Publishing Ltd. 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 pr. 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 pr 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.

Source or Periodical Title

Journal of Physics: Conference Series

ISSN

17426588

Document Type

Article

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