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Four classes of minimal binary linear codes with \(w_{min}/w_{max}<1/2\) derived from Boolean functions

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Abstract

Due to wide applications in communications, data storage, and cryptography, linear codes have received much attention in the past decades. As a subclass of linear codes, minimal linear codes can be used to construct secret sharing schemes with nice access structure. This paper gives the weight distributions of four classes of minimal binary linear codes with \(w_{min}/w_{max}<1/2\) derived from Boolean functions.

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Authors and Affiliations

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

    Xia Li & Qin Yue

  2. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, People’s Republic of China

    Xia Li & Qin Yue

Authors
  1. Xia Li
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  2. Qin Yue
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Correspondence to Xia Li.

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Communicated by C. Ding.

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The paper was supported by National Natural Science Foundation of China (No. 61772015).

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Li, X., Yue, Q. Four classes of minimal binary linear codes with \(w_{min}/w_{max}<1/2\) derived from Boolean functions. Des. Codes Cryptogr. 88, 257–271 (2020). https://doi.org/10.1007/s10623-019-00682-1

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  • DOI: https://doi.org/10.1007/s10623-019-00682-1

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