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MDS codes with l-Galois hulls of arbitrary dimensions

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Abstract

The hull of a linear code is defined to be the intersection of the code and its dual, and was originally introduced to classify finite projective planes. The objective of this paper is to construct some MDS codes with l-Galois hulls of arbitrary dimensions by using the generalized Reed–Solomon codes over finite fields with regard to l-Galois inner product. We give a general construction theorem and some construction ideas of MDS with l-Galois hulls of arbitrary dimensions. Our approach provides a general framework that effectively unifies similar known techniques for constructing MDS codes.

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Acknowledgements

This research was supported in part by the National Natural Science Foundation of China under Grants 12301663, 12171241 and 12226408, in part by the Natural Science Foundation of Anhui Province under Grant 2308085QA10 and in part by the China Postdoctoral Science Foundation under Grant 2023M740016.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, Anhui, China

    Liqin Qian

  2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210007, Jiangsu, China

    Xiwang Cao

  3. Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100042, China

    Xiwang Cao

  4. School of Mathematics, Southeast University, Nanjing, 211189, Jiangsu, China

    Xia Wu & Wei Lu

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  1. Liqin Qian
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  2. Xiwang Cao
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  3. Xia Wu
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  4. Wei Lu
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Correspondence to Liqin Qian.

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Communicated by G. Lunardon.

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Qian, L., Cao, X., Wu, X. et al. MDS codes with l-Galois hulls of arbitrary dimensions. Des. Codes Cryptogr. (2024). https://doi.org/10.1007/s10623-024-01371-4

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  • DOI: https://doi.org/10.1007/s10623-024-01371-4

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