Some constacyclic BCH codes with good parameters (original) (raw)

Abstract

BCH codes as a subclass of constacyclic BCH codes have been widely studied, while the results on the parameters of BCH codes over finite fields are still very limited. In this paper, we investigate some _q_-ary BCH codes and \(\lambda \)-constacyclic BCH codes of length \(q^{m}+1\), where q is a prime power and \(\textrm{ord}(\lambda )\mid q-1\). We determine the dimensions of these codes with some large designed distances, and give good lower bounds on the minimum distance. The code examples presented in this paper indicate that these codes contain many distance-optimal codes and codes with best known parameters.

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Acknowledgements

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

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230601, Anhui, China
    Jin Li & Huilian Zhu
  2. Department of Information Management, Anhui Vocational College of Police Officers, Hefei, 230031, Anhui, China
    Shan Huang

Authors

  1. Jin Li
  2. Huilian Zhu
  3. Shan Huang

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These authors contributed equally to this work.

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Correspondence toHuilian Zhu.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Communicated by C. Ding.

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The work was supported by the National Natural Science Foundation of China (No.62002093, No.12171134, No.U21A20428) and the Fundamental Research Funds for the Central Universities of China (No.JZ2022HGTB0264) and the Key Projects of Natural Science Research of Universities in Anhui Province (No.KJ2021A1469).

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Li, J., Zhu, H. & Huang, S. Some constacyclic BCH codes with good parameters.Des. Codes Cryptogr. 92, 3237–3259 (2024). https://doi.org/10.1007/s10623-024-01433-7

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