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More classes of optimal quinary cyclic codes of form \({\mathcal {C}}_{(1,e,s)}\)

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Abstract

Cyclic codes are an important subclass of linear codes. In this paper, we investigate the construction of quinary cyclic codes with parameters \([5^{m}-1, 5^{m}-2m-2, 4]\) and eight new classes optimal quinary cyclic codes of form \({\mathcal {C}}_{(1,e,s)}\) are presented by discussing the solutions of certain equations over \({\mathbb {F}}_{5^{m}}\).

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Authors and Affiliations

  1. College of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, 224003, China

    Yan Liu

  2. School of Mathematical Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Xiwang Cao

  3. Key Laboratory of Mathematical Modeling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing, 210016, China

    Xiwang Cao

  4. School of Mathematical Sciences, Luoyang Normal University, Luoyang, 471934, China

    Zhengbang Zha

Authors
  1. Yan Liu
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  2. Xiwang Cao
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  3. Zhengbang Zha
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Correspondence to Yan Liu.

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Y. Liu is supported by the National Natural Science Foundation of China (No.12001475), Natural Science Foundation of Jiangsu Province (No. BK20201059). X. Cao is supported by the National Natural Science Foundation of China (No. 12171241). Z. Zha is supported by the National Natural Science Foundation of China (No. 62072222).

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Liu, Y., Cao, X. & Zha, Z. More classes of optimal quinary cyclic codes of form \({\mathcal {C}}_{(1,e,s)}\). AAECC (2023). https://doi.org/10.1007/s00200-023-00604-8

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  • DOI: https://doi.org/10.1007/s00200-023-00604-8

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