On $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-$(1+u)$-additive constacyclic

Ping Li; Wei Dai; Xiaoshan Kai

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arXiv · 1611.03169

On $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-$(1+u)$-additive constacyclic

Ping Li·Wei Dai·Xiaoshan Kai

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Abstract

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.

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Ping Li, Wei Dai, Xiaoshan Kai. 2016-11-10. On $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-$(1+u)$-additive constacyclic. https://arxiv.org/abs/1611.03169

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