In this work, we introduce the \({\mathbb {F}}_qR\)-linear skew cyclic codes, wh ere \(q=p^s\) is a prime power and \(R={\mathbb {F}}_q+u{\mathbb {F}}_q\) with \(u^2=0\). We provide the algebraic structure of these codes. The dual codes of separable linear skew cyclic codes are also presented. Finally, by using the Gray map from \({\mathbb {F}}_qR\) to \({\mathbb {F}}_q\), we get some optimal linear codes over \({\mathbb {F}}_q\).

中文翻译：

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$${\mathbb {F}}_qR$$ F q R -Linear skew 循环码

在这项工作中，我们引入了\({\mathbb {F}}_qR\) -linear skew 循环码，其中\(q=p^s\)是素数幂，而\(R={\mathbb {F }}_q+u{\mathbb {F}}_q\)与\(u^2=0\)。我们提供这些代码的代数结构。还给出了可分离线性偏斜循环码的对偶码。最后，通过使用从\({\mathbb {F}}_qR\)到\({\mathbb {F}}_q\)的格雷图，我们得到了一些关于\({\mathbb {F}} _q\)。