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\(\pmb {{\mathbb {F}}}_q\)-Linear skew cyclic codes over \(\pmb {{\mathbb {F}}}_{q^2}\) and their applications of quantum codes construction

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Abstract

In this paper, we study the structure of \({\mathbb {F}}_q\)-linear skew cyclic codes over \({\mathbb {F}}_{q^2}\). Some good \({\mathbb {F}}_q\)-linear skew cyclic codes over \({\mathbb {F}}_{q^2}\) are constructed. Moreover, as an application, some good quantum codes are obtained by \({\mathbb {F}}_q\)-linear skew cyclic codes over \({\mathbb {F}}_{q^2}\).

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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 Nos. 11671024, 61571243, 11701336, 11626144 and 11671235), the Fundamental Research Funds for the Central Universities of China, the Scientific Research Fund of Hubei Provincial Key Laboratory of Applied Mathematics (Hubei University)(Grant No. HBAM201804), the Scientific Research Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Changsha University of Science and Technology)(Grant No. 2018MMAEZD04), the Beijing Postdoctoral Research Foundation, and the Chaoyang Postdoctoral Research Foundation.

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Authors and Affiliations

  1. College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, 100124, China

    Yun Gao & Shilin Yang

  2. School of Science, Shandong University of Technology, Zibo, 255000, China

    Jian Gao

  3. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

    Jian Gao

  4. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, China

    Jian Gao

  5. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China

    Fang-Wei Fu

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  1. Yun Gao
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  2. Jian Gao
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  4. Fang-Wei Fu
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Correspondence to Yun Gao.

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Gao, Y., Gao, J., Yang, S. et al. \(\pmb {{\mathbb {F}}}_q\)-Linear skew cyclic codes over \(\pmb {{\mathbb {F}}}_{q^2}\) and their applications of quantum codes construction. J. Appl. Math. Comput. 68, 349–361 (2022). https://doi.org/10.1007/s12190-020-01479-5

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  • DOI: https://doi.org/10.1007/s12190-020-01479-5

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