$(1-2u^k)$-constacyclic codes over $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_+u^{3}\mathbb{F}_{p}+\dots+u^{k}\mathbb{F}_{p}$

Zahid Raza; Amrina Rana

$(1-2u^k)$-constacyclic codes over $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_+u^{3}\mathbb{F}_{p}+\dots+u^{k}\mathbb{F}_{p}$

Information Theory 2019-04-18 v2 math.IT

Authors: Zahid Raza , Amrina Rana

Abstract

Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^k)$ -constacyclic codes over the ring $\mathcal{R}=\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p+u^{3}\mathbb{F}_{p}+\cdots+u^{k}\mathbb{F}_{p}$ where $u^{k+1}=u$ . We illustrate the generator polynomials and investigate the structural properties of these codes via decomposition theorem.

Keywords

constacyclic codes finite ring generator polynomials decomposition theorem structural properties

Cite

@article{arxiv.1512.02332,
  title  = {$(1-2u^k)$-constacyclic codes over $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_+u^{3}\mathbb{F}_{p}+\dots+u^{k}\mathbb{F}_{p}$},
  author = {Zahid Raza and Amrina Rana},
  journal= {arXiv preprint arXiv:1512.02332},
  year   = {2019}
}

Related papers

View all related →