Can I read On $\mathbb{Z} {2}\mathbb{Z} {2}[u]$-$(1+u)$-additive constacyclic on EtoBox?

On $\mathbb{Z} {2}\mathbb{Z} {2}[u]$-$(1+u)$-additive constacyclic by Li, Ping; Dai, Wei; Kai, Xiaoshan is a scholarly article available to read on EtoBox.

What is On $\mathbb{Z} {2}\mathbb{Z} {2}[u]$-$(1+u)$-additive constacyclic about?

In this paper, we study $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-$(1+u)$-additive constacyclic code of arbitrary length. Firstly, we study the algebraic structure of this family of codes and a set of generator polynomials for this family as a $(\mathbb{Z}_{2}+u\mathbb{Z}_{2})[x]$-submodule of the ring $R_{\alpha,\beta}$. Secondly, we give the minimal generating sets of this family codes, and we determine the relationship of generators between the $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-$(1+u)$-additive constacyclic codes and its dual and give the parameters in terms of the degrees of the generator polynomials of the code. Lastly, we also study $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-$(1+u)$-additive constacyclic code in terms of the Gray images.

Author

Li, Ping; Dai, Wei; Kai, Xiaoshan

Published

2016

Language

EN