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arXiv · 1610.00900

Self-Dual Codes over $\mathbb{Z}_2\times (\mathbb{Z}_2+u\mathbb{Z}_2)$

Long Yu·Qiong Huang·Hongwei Liu·Xiusheng Liu
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Abstract

In this paper, we study self-dual codes over $\mathbb{Z}_2 \times (\mathbb{Z}_2+u\mathbb{Z}_2) $, where $u^2=0$. Three types of self-dual codes are defined. For each type, the possible values $\alpha,\beta$ such that there exists a code $\mathcal{C}\subseteq \mathbb{Z}_{2}^\alpha\times (\mathbb{Z}_2+u\mathbb{Z}_2)^\beta$ are established. We also present several approaches to construct self-dual codes over $\mathbb{Z}_2 \times (\mathbb{Z}_2+u\mathbb{Z}_2) $. Moreover, the structure of two-weight self-dual codes is completely obtained for $\alpha \cdot\beta\neq 0$.

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Long Yu, Qiong Huang, Hongwei Liu, Xiusheng Liu. 2016-10-04. Self-Dual Codes over $\mathbb{Z}_2\times (\mathbb{Z}_2+u\mathbb{Z}_2)$. https://arxiv.org/abs/1610.00900

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