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

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 $\alpha \cdot \beta \ne 0$.

arXiv comment18 pages

References in corpus (2)

• Z2Z4-linear codes: generator matrices and duality
• Self-Dual Codes over Z_2xZ_4