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On some conjectures about optimal ternary cyclic codes

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, by investigating the solutions of certain equations over finite fields, we make progress towards three conjectures about optimal ternary cyclic codes which were proposed by Ding and Helleseth.

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Acknowledgements

The authors are grateful to the two anonymous reviewers and the editor for their detailed comments and suggestions which highly improve the presentation and quality of this paper. They also would like to thank Chunlei Li for some useful suggestions to improve the writing. This work was supported by the Talent Fund project of Fuzhou University under Grant number 0030510858

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350108, China

    Qian Liu & Ximeng Liu

  2. Key Lab of Information Security of Network Systems, Fuzhou University, Fuzhou, 350108, China

    Qian Liu & Ximeng Liu

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  1. Qian Liu
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  2. Ximeng Liu
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Correspondence to Qian Liu.

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Liu, Q., Liu, X. On some conjectures about optimal ternary cyclic codes . AAECC 33, 419–436 (2022). https://doi.org/10.1007/s00200-020-00458-4

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  • DOI: https://doi.org/10.1007/s00200-020-00458-4

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