Some properties of dihedral group codes
Rings and Algebras
2021-03-02 v3 Information Theory
math.IT
Abstract
In this paper, we study the dihedral codes, i.e. the left ideals of in the case . An explicit algebraic description of the dihedral codes and their duals is obtained. In addition, a criterion for self-duality of a dihedral code is obtained. Bases, generating and check matrices of dihedral codes are constructed. Given a dihedral code, we consider exterior and interior codes that are induced by cyclic codes. Using this codes, some properties of generating matrices are described and a connection to cyclic code theory is established. In addition, some estimates of code parameters are obtained and several illustrative examples are given.
Cite
@article{arxiv.2005.08283,
title = {Some properties of dihedral group codes},
author = {Kirill V. Vedenev and Vladimir M. Deundyak},
journal= {arXiv preprint arXiv:2005.08283},
year = {2021}
}