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Minimal linear codes constructed from partial spreads

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Abstract

Partial spreads are important in finite geometry and can be used to construct linear codes. From the results in (Des. Codes Cryptogr.90, 1–15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a partial spread is “big enough”, then the corresponding linear code is minimal. This paper used the sufficient condition in (IEEE Trans. Inf. Theory44(5), 2010–2017, 1998) to prove the minimality of such linear codes. In the present paper, we use the geometric approach to study the minimality of linear codes constructed from partial spreads in all cases.

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Author information

Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 210096, China

    Xia Wu & Wei Lu

  2. School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, China

    Xiwang Cao

  3. School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), Nanyang, 637371, Singapore

    Gaojun Luo

Authors
  1. Xia Wu

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  2. Wei Lu

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  3. Xiwang Cao

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  4. Gaojun Luo

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Contributions

Xia Wu and Wei Lu wrote the manuscript text and gave the proof of Theorem 3.3, 3.4 and 3.6. Xiwang Cao and Gaojun Luo gave the proof of Theorem of 3.8. All authors reviewed the manuscript.

Corresponding author

Correspondence toWei Lu.

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The authors declare no competing interests.

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Supported by NSFC (Nos. 12371035, 11971102, 12171241), the Fundamental Research Funds for the Central Universities.

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Wu, X., Lu, W., Cao, X.et al. Minimal linear codes constructed from partial spreads.Cryptogr. Commun.16, 601–611 (2024). https://doi.org/10.1007/s12095-023-00689-5

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