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Parameters of several families of binary duadic codes and their related codes

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Abstract

Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length \(2^m-1\) and develop some lower bounds on their minimum distances by using the BCH bound on cyclic codes, which partially solves one case of the open problem proposed in Liu et al (Finite Field Appl 91:102270, 2023). It is shown that the lower bounds on their minimum distances are close to the square root bound. Moreover, the parameters of the dual and extended codes of these binary duadic codes are investigated.

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Acknowledgements

The authors are very grateful to the reviewers and the editor for their detailed comments and suggestions that much improved the presentation and quality of this paper.

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Authors and Affiliations

  1. MoE Engineering Research Center of Software/Hardware Co-design Technology and Application, East China Normal University, Shanghai, 200062, China

    Hai Liu & Chengju Li

  2. National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, China

    Hai Liu & Chengju Li

  3. School of Software Engineering, East China Normal University, Shanghai, 200062, China

    Haifeng Qian

Authors
  1. Hai Liu
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  2. Chengju Li
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  3. Haifeng Qian
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Correspondence to Chengju Li.

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Communicated by J.-L. Kim.

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The work of Hai Liu and Chengju Li was supported by the National Natural Science Foundation of China (12071138), Shanghai Natural Science Foundation (22ZR1419600), the open research fund of National Mobile Communications Research Laboratory of Southeast University (2022D05). The work of Haifeng Qian was supported by the Innovation Program of Shanghai Municipal Education Commission (2021-01-07-00-08-E00101), and “Digital Silk Road” Shanghai International Joint Lab of Trustworthy Intelligent Software (22510750100).

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Liu, H., Li, C. & Qian, H. Parameters of several families of binary duadic codes and their related codes. Des. Codes Cryptogr. 92, 1–12 (2024). https://doi.org/10.1007/s10623-023-01285-7

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  • DOI: https://doi.org/10.1007/s10623-023-01285-7

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