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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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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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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DOI: https://doi.org/10.1007/s10623-023-01184-x