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Linear codes with few weights from cyclotomic classes and weakly regular bent functions

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Abstract

Linear codes with few weights constructed from defining sets have been extensively studied due to their applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Li et al. (Appl Algebra Eng Commun Comput 28(1):11–30, 2017) and Jian et al. (Finite Fields Appl 57:92–107, 2019), we propose a class of five-weight linear codes by choosing the defining set from cyclotomic classes, which includes a class of two-weight linear codes as a special case, and we also present two classes of two or three-weight linear codes by employing weakly regular bent functions. Besides, we obtain a class of two-weight optimal punctured codes with respect to the Griesmer bound.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 61702166, 61761166010) and Major Technological Innovation Special Project of Hubei Province (No. 2019ACA144).

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Authors and Affiliations

  1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

    Yanan Wu, Nian Li & Xiangyong Zeng

  2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China

    Yanan Wu, Nian Li & Xiangyong Zeng

Authors
  1. Yanan Wu
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  2. Nian Li
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  3. Xiangyong Zeng
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Correspondence to Nian Li.

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Communicated by V. D. Tonchev.

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Wu, Y., Li, N. & Zeng, X. Linear codes with few weights from cyclotomic classes and weakly regular bent functions. Des. Codes Cryptogr. 88, 1255–1272 (2020). https://doi.org/10.1007/s10623-020-00744-9

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  • DOI: https://doi.org/10.1007/s10623-020-00744-9

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