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 $\alpha \cdot\beta\neq 0$.
Categories: cs.IT math.IT