English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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 codesare defined. For each type, the possible values $\alpha,\beta$ such that thereexists a code $\mathcal{C}\subseteq \mathbb{Z}_{2}^\alpha\times(\mathbb{Z}_2+u\mathbb{Z}_2)^\beta$ are established. We also present severalapproaches to construct self-dual codes over $\mathbb{Z}_2 \times(\mathbb{Z}_2+u\mathbb{Z}_2) $. Moreover, the structure of two-weight self-dualcodes is completely obtained for $\alpha \cdot\beta\neq 0$.

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