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Designed distances and parameters of new LCD BCH codes over finite fields

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Abstract

Let \(\mathbb {F}_{q}\) be the finite field of q elements and n = qm − 1 with m a positive integer. In this paper we construct a class of BCH and LCD BCH codes of length n over \(\mathbb {F}_{q}\) and investigate their dimensions and designed distance. Our results show that the designed distances of BCH and LCD BCH codes in this paper are larger than those in [11, Theorems 7, 10, 18, and 22]. It is viewed as a generalized result of [11].

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Acknowledgments

The paper was supported by National Natural Science Foundation of China under Grants 11601475, 61772015 and Foundation of Science and Technology on Information Assurance Labo- ratory under Grant KJ-17-010.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, People’s Republic of China

    Fengwei Li

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

    Fengwei Li

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

    Qin Yue & Yansheng Wu

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  1. Fengwei Li
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  2. Qin Yue
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  3. Yansheng Wu
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Correspondence to Fengwei Li.

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Li, F., Yue, Q. & Wu, Y. Designed distances and parameters of new LCD BCH codes over finite fields. Cryptogr. Commun. 12, 147–163 (2020). https://doi.org/10.1007/s12095-019-00385-3

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  • DOI: https://doi.org/10.1007/s12095-019-00385-3

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Mathematics Subject Classification (2010)