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A family of optimal ternary cyclic codes with minimum distance five and their duals

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Abstract

As a subclass of linear codes, cyclic codes have important applications in consumer electronics, data storage systems and communication systems. In this paper, a new family of optimal ternary cyclic codes with minimum distance five are obtained from known perfect nonlinear functions over \(\mathbb {F}_{3^{m}}\). Moreover, we investigate the weight distributions of their duals.

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Acknowledgements

This work was supported by the National Natural Science Foundations of China (Grant Nos. 11771007 and 61572027)

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, 211100, Nanjing, People’s Republic of China

    Dandan Wang & Xiwang Cao

  2. State Key Laboratory of Information Security Institute of Information Engineering, Chinese Academy of Sciences, 100093, Beijing, China

    Xiwang Cao

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  1. Dandan Wang
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  2. Xiwang Cao
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Correspondence to Xiwang Cao.

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This article belongs to the Topical Collection: Sequences and Their Applications III

Guest Editors: Chunlei Li, Tor Helleseth and Zhengchun Zhou

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Wang, D., Cao, X. A family of optimal ternary cyclic codes with minimum distance five and their duals. Cryptogr. Commun. 14, 1–13 (2022). https://doi.org/10.1007/s12095-021-00493-z

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