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Construction of Two Classes of Minimal Binary Linear Codes Based on Boolean Function

Jiawei DU, Xiaoni DU, Wengang JIN, Yingzhong ZHANG

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Summary :

Linear codes with a few-weight have important applications in combinatorial design, strongly regular graphs and cryptography. In this paper, we first construct a class of Boolean functions with at most five-valued Walsh spectra, and determine their spectrum distribution. Then, we derive two classes of linear codes with at most six-weight from the new functions. Meanwhile, the length, dimension and weight distributions of the codes are obtained. Results show that both of the new codes are minimal and among them, one is wide minimal code and the other is a narrow minimal code and thus can be used to design secret sharing scheme with good access structures. Finally, some Magma programs are used to verify the correctness of our results.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.4 pp.689-693
Publication Date
2022/04/01
Publicized
2021/09/30
Online ISSN
1745-1337
DOI
10.1587/transfun.2021EAP1062
Type of Manuscript
PAPER
Category
Cryptography and Information Security

Authors

Jiawei DU
  Northwest Normal University,Guilin University of Electronic Technology
Xiaoni DU
  Northwest Normal University
Wengang JIN
  Northwest Normal University
Yingzhong ZHANG
  Northwest Normal University

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