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Hulls of cyclic codes with respect to the regular permutation inner product

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Abstract

In this paper, we introduce regular permutation inner products which contain the Euclidean inner product. And we generalize some properties of the Euclidean inner product to regular permutation inner products. As application, we construct a lot of cyclic codes with specific regular permutation hulls and also obtain the dimensions and distances of some BCH codes.

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Authors and Affiliations

  1. Center for Applied Mathematics of Guangxi, Nanning Normal University, Nanning, 530023, People’s Republic of China

    Xiaoshan Quan

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

    Qin Yue & Fuqing Sun

  3. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, People’s Republic of China

    Qin Yue & Fuqing Sun

Authors
  1. Xiaoshan Quan
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  2. Qin Yue
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  3. Fuqing Sun
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Corresponding author

Correspondence to Qin Yue.

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Communicated by J. Bierbrauer.

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The paper is supported by National Natural Science Foundation of China (Nos. 62172219 and 12171420), Natural Science Foundation of Shandong Province under Grant ZR2021MA046, Natural Science Foundation of Jiangsu Province under Grant BK20200268, Research Foundation Ability Enhancement Project for Young and Middle aged Teachers in Guangxi Universities 2024KY0408.

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Quan, X., Yue, Q. & Sun, F. Hulls of cyclic codes with respect to the regular permutation inner product. Des. Codes Cryptogr. 92, 3063–3083 (2024). https://doi.org/10.1007/s10623-024-01428-4

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  • DOI: https://doi.org/10.1007/s10623-024-01428-4

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