Some results about double cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^2\mathbb{F}_{q}$
Information Theory
2021-03-11 v1 math.IT
Rings and Algebras
Abstract
Let be the finite field with elements. This paper mainly researches the polynomial representation of double cyclic codes over with . Firstly, we give the generating polynomials of these double cyclic codes. Secondly, we show the generating matrices of them. Meanwhile, we get quantitative information related to them by the matrix forms. Finally, we investigate the relationship between the generators of double cyclic codes and their duals.
Cite
@article{arxiv.2103.05859,
title = {Some results about double cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^2\mathbb{F}_{q}$},
author = {Tenghui Deng and Jing Yang},
journal= {arXiv preprint arXiv:2103.05859},
year = {2021}
}