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MDS and near-MDS codes via twisted Reed–Solomon codes

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Abstract

Maximum distance separable (MDS) codes are optimal in the sense that the minimum distance cannot be improved for a given length and code size. Twisted Reed–Solomon codes come from Reed–Solomon codes by adding a monomial. In this paper, we give a necessary and sufficient condition that twisted Reed–Solomon codes are MDS (near-MDS). Moreover, we prove that a lot of MDS codes, which are constructed via twisted Reed–Solomon codes, are not equivalent to Reed–Solomon codes.

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Acknowledgements

The authors are very grateful to the reviewers and the editor for their valuable comments and suggestions to improve the quality of this paper. This work is supported in part by the National Natural Science Foundation of China (Nos. 62172219, 61772015, 12071138, and 12001396), the Natural Science Foundation of Jiangsu Province of China (No. BK20200268), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 20KJB110005) and Qing Lan Project of the Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, People’s Republic of China

    Junzhen Sui

  2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, People’s Republic of China

    Xiaomeng Zhu

  3. Department of Mathematics, Taizhou University, Taizhou, 225300, People’s Republic of China

    Xueying Shi

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  1. Junzhen Sui
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  2. Xiaomeng Zhu
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  3. Xueying Shi
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Correspondence to Xiaomeng Zhu.

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Communicated by T. Feng.

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This work is supported in part by the National Natural Science Foundation of China (Nos. 62172219, 61772015, 12071138, and 12001396), the Natural Science Foundation of Jiangsu Province of China (No. BK20200268), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 20KJB110005) and Qing Lan Project of the Jiangsu Higher Education Institutions.

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Sui, J., Zhu, X. & Shi, X. MDS and near-MDS codes via twisted Reed–Solomon codes. Des. Codes Cryptogr. 90, 1937–1958 (2022). https://doi.org/10.1007/s10623-022-01049-9

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  • DOI: https://doi.org/10.1007/s10623-022-01049-9

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