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Cyclic codes of length 5p with MDS symbol-pair

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Abstract

Let p be a prime with \(5 |(p-1)\). Let S be a set of all repeated-root cyclic codes \({\mathcal {C}}=\langle g(x)\rangle \), \((x^5-1)|g(x)\), of length 5p over a field field \({\mathbb {F}}_p\), whose Hamming distances are at most 7. In this paper, we present a method to find all maximum distance separable (MDS) symbol-pair codes in S. By this method we can easily obtain the results in Ma and Luo (Des Codes Cryptogr 90:121–137, 2022) and new MDS symbol-pair codes, so we remain two possible MDS symbol-pair codes for readers.

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Acknowledgements

The author is very grateful to the reviewers and the editor for their valuable comments and suggestions that much improved the quality of this paper.

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Authors and Affiliations

  1. College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, People’s Republic of China

    Fengwei Li

  2. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, People’s Republic of China

    Fengwei Li

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  1. Fengwei Li
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Correspondence to Fengwei Li.

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Communicated by G. Ge

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The paper was supported by National Natural Science Foundation of China under Grant 12171420, Natural Science Foundation of Shandong Province under Grant ZR2021MA046, and Plateau science of Zaozhuang University.

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Li, F. Cyclic codes of length 5p with MDS symbol-pair. Des. Codes Cryptogr. 91, 1873–1888 (2023). https://doi.org/10.1007/s10623-023-01184-x

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