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\({\mathbb {F}}_qR\)-Linear skew cyclic codes

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Abstract

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 \({\mathbb {F}}_q\).

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Acknowledgements

This research is supported by the 973 Program of China (Grant No. 2013CB834204), the National Natural Science Foundation of China (Grant No. 61571243, 12071264, 11701336, 11626144 and 11671235), the Fundamental Research Funds for the Central Universities of China.

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Authors and Affiliations

  1. Chern Institute of Mathematics and LPMC, and Tianjin Key Laboratory of Network and Data Security Technology, Nankai University, Tianjin, 300071, China

    Juan Li & Fang-Wei Fu

  2. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255091, Shandong, China

    Jian Gao

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  1. Juan Li
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Correspondence to Jian Gao.

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Li, J., Gao, J. & Fu, FW. \({\mathbb {F}}_qR\)-Linear skew cyclic codes. J. Appl. Math. Comput. 68, 1719–1741 (2022). https://doi.org/10.1007/s12190-021-01588-9

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