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Ternary self-orthogonal codes from weakly regular bent functions and their application in LCD Codes

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Abstract

Self-orthogonal codes are linear codes such that they are contained in their duals. Self-orthogonal codes have attracted much attention due to their applications in linear complementary dual codes (LCD codes for short), quantum codes, row-self-orthogonal matrices and so on. In this paper, we first construct several families of ternary self-orthogonal codes from weakly regular bent functions. The parameters and weight distributions of them are determined. Then we use the self-orthogonal codes to construct new infinite families of ternary LCD codes. Some LCD codes are optimal according to the Code Tables at http://www.codetables.de/.

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Acknowledgements

The authors are very grateful to the reviewers and the Editor for their constructive suggestions which greatly improve the quality of this paper.

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Authors and Affiliations

  1. School of Science, Chang’an University, Xi’an, 710064, China

    Ziling Heng, Dexiang Li & Fenjin Liu

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  1. Ziling Heng
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  2. Dexiang Li
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  3. Fenjin Liu
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Correspondence to Dexiang Li.

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Communicated by T. Helleseth.

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Z. Heng’s research was supported in part by the National Natural Science Foundation of China under Grant 12271059, in part by the Young Talent Fund of University Association for Science and Technology in Shaanxi, China, under Grant 20200505, and in part by the Fundamental Research Funds for the Central Universities, CHD, under Grant 300102122202

F. Liu’s research was supported in part by Natural Science Basic Research Program of Shaanxi under Grant 2021JM-149.

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Heng, Z., Li, D. & Liu, F. Ternary self-orthogonal codes from weakly regular bent functions and their application in LCD Codes. Des. Codes Cryptogr. 91, 3953–3976 (2023). https://doi.org/10.1007/s10623-023-01287-5

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  • DOI: https://doi.org/10.1007/s10623-023-01287-5

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