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Minimal linear codes from weakly regular bent functions

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Abstract

Minimal linear codes have received much attention in the past decades due to their important applications in secret sharing schemes and secure two-party computation, etc. Recently, several classes of minimal linear codes with \(w_{\min \limits }/w_{\max \limits }\leq (p-1)/p\) have been discovered, where \(w_{\min \limits }\) and \(w_{\max \limits }\) respectively denote the minimum and maximum nonzero weights in a code. In this paper, we investigate the minimality of a class of p-ary linear codes and obtain some sufficient conditions for this kind of linear codes to be minimal, which is a generalization of the recent results given by Xu et al. (Finite Fields Appl. 65,101688, 32). This allows us to construct new minimal linear codes with \(w_{\min \limits }/w_{\max \limits }\leq (p-1)/p\) from weakly regular bent functions for the first time. The parameters of minimal linear codes presented in this paper are different from those known in the literature.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 62172183, 11601177, 61722213, 12171241), the Natural Science Foundation for the Higher Education Institutions of Anhui Province of China (Nos. KJ2020A0643, KJ2020A0780) and Program for Innovative Research Team in Huainan Normal University (No. XJTD202008).

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Authors and Affiliations

  1. School of Finance and Mathematics, Huainan Normal University, 232038, Huainan, China

    Guangkui Xu

  2. College of Liberal Arts and Science, National University of Defense Technology, 410073, Changsha, China

    Longjiang Qu

  3. School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore, Singapore

    Gaojun Luo

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  1. Guangkui Xu
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  2. Longjiang Qu
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  3. Gaojun Luo
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Correspondence to Guangkui Xu.

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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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Xu, G., Qu, L. & Luo, G. Minimal linear codes from weakly regular bent functions. Cryptogr. Commun. 14, 415–431 (2022). https://doi.org/10.1007/s12095-021-00519-6

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