A Circulant Approach to Skew-Constacyclic Codes
Information Theory
2014-09-30 v2 math.IT
Rings and Algebras
Abstract
We introduce circulant matrices that capture the structure of a skew-polynomial ring F[x;\theta] modulo the left ideal generated by a polynomial of the type x^n-a. This allows us to develop an approach to skew-constacyclic codes based on such circulants. Properties of these circulants are derived, and in particular it is shown that the transpose of a certain circulant is a circulant again. This recovers the well-known result that the dual of a skew-constacyclic code is a constacyclic code again. Special attention is paid to the case where x^n-a is two-sided.
Keywords
Cite
@article{arxiv.1408.5445,
title = {A Circulant Approach to Skew-Constacyclic Codes},
author = {Neville Fogarty and Heide Gluesing-Luerssen},
journal= {arXiv preprint arXiv:1408.5445},
year = {2014}
}