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

Let $\mathbb{F}_q$ be a finite field of order $q$, a prime power integer suchthat $q=et+1$ where $t\geq 1,e\geq 2$ are integers. In this paper, we studycyclic codes of length $n$ over a non-chain ring$R_{e,q}=\mathbb{F}_q[u]/\langle u^e-1\rangle$. We define a Gray map $\varphi$and obtain many { maximum-distance-separable} (MDS) and optimal$\mathbb{F}_q$-linear codes from the Gray images of cyclic codes. Under certainconditions we determine { linear complementary dual} (LCD) codes of length $n$when $\gcd(n,q)\neq 1$ and $\gcd(n,q)= 1$, respectively. It is proved that { a}cyclic code $\mathcal{C}$ of length $n$ is an LCD code if and only if its Grayimage $\varphi(\mathcal{C})$ is an LCD code of length $4n$ over $\mathbb{F}_q$.Among others, we present the conditions for existence of free and non-free LCDcodes. Moreover, we obtain many optimal LCD codes as the Gray images ofnon-free LCD codes over $R_{e,q}$.

Cyclic codes over a non-chain ring $R_{e,q}$ and their application to LCD codes