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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We introduce a Gray map from $\mathbb{F}_{2^{m}}+u\mathbb{F}_{2^{m}}$ to$\mathbb{F}_{2}^{2m}$ and study $(1+u)$-constacyclic codes over$\mathbb{F}_{2^{m}}+u\mathbb{F}_{2^{m}},$ where $u^{2}=0.$ It is proved thatthe image of a $(1+u)$-constacyclic code length $n$ over$\mathbb{F}_{2^{m}}+u\mathbb{F}_{2^{m}}$ under the Gray map is adistance-invariant quasi-cyclic code of index $m$ and length $2mn$ over$\mathbb{F}_{2}.$ We also prove that every code of length $2mn$ which is theGray image of cyclic codes over $\mathbb{F}_{2^{m}}+u\mathbb{F}_{2^{m}}$ oflength $n$ is permutation equivalent to a binary quasi-cyclic code of index$m.$ Furthermore, a family of quantum error-correcting codes obtained from theCalderbank-Shor-Steane (CSS) construction applied to $(1+u)$-constacyclic codesover $\mathbb{F}_{2^{m}}+u\mathbb{F}_{2^{m}}.$

A family of constacyclic codes over $\mathbb{F}_{2^{m}}+u\mathbb{F}_{2^{m}}$ and its application to quantum codes