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Hermitian LCD codes from cyclic codes

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Abstract

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. It was proved that asymptotically good Hermitian LCD codes exist. The objective of this paper is to construct some cyclic Hermitian LCD codes over finite fields and analyse their parameters. The dimensions of these codes are settled and the lower bounds on their minimum distances are presented. Most Hermitian LCD codes presented in this paper are not BCH codes.

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Acknowledgements

The author is very grateful to the editor and the reviewers for their detailed comments and suggestions that much improved the presentation and quality of this paper. The author would also like to thank Prof. Cunsheng Ding for his kind help to complete this work.

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Authors and Affiliations

  1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China

    Chengju Li

Authors
  1. Chengju Li
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Correspondence to Chengju Li.

Additional information

Communicated by P. Charpin.

The work was supported by the National Natural Science Foundation of China (NSFC) under Grant 11701179 and the Shanghai Sailing Program under Grant 17YF1404300.

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Li, C. Hermitian LCD codes from cyclic codes. Des. Codes Cryptogr. 86, 2261–2278 (2018). https://doi.org/10.1007/s10623-017-0447-0

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  • DOI: https://doi.org/10.1007/s10623-017-0447-0

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