English

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 Fq\mathbb{F}_{q} be the finite field with qq elements. This paper mainly researches the polynomial representation of double cyclic codes over Fq+vFq+v2Fq\mathbb{F}_{q}+v\mathbb{F}_{q}+v^2\mathbb{F}_{q} with v3=vv^3=v. 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.

Keywords

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}
}