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Some new bounds on LCD codes over finite fields

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Abstract

In this paper, we show that LCD codes are not equivalent to non-LCD codes over small finite fields. The enumeration of binary optimal LCD codes is obtained. We also get the exact value of LD(n,2) over \(\mathbb {F}_{3}\) and \(\mathbb {F}_{4}\), where LD(n,2) := max{d∣thereexsitsan [n,2, d] LCD\( code~ over~ \mathbb {F}_{q}\}\). We study the bound of LCD codes over \(\mathbb {F}_{q}\) and generalize a conjecture proposed by Galvez et al. about the minimum distance of binary LCD codes.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China Grant Nos 61772168 and 11501156 and the Fundamental Research Funds for the Central Universities of China Grant No. PA2019GDZC0097. The authors would like to thank the Editor-in-Chief Claude Carlet and anonymous referees for the useful comments.

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230009, Anhui, People’s Republic of China

    Binbin Pang, Shixin Zhu & Xiaoshan Kai

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  1. Binbin Pang
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  2. Shixin Zhu
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  3. Xiaoshan Kai
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Correspondence to Shixin Zhu.

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Pang, B., Zhu, S. & Kai, X. Some new bounds on LCD codes over finite fields. Cryptogr. Commun. 12, 743–755 (2020). https://doi.org/10.1007/s12095-019-00417-y

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