Construction of Two Classes of Minimal Binary Linear Codes

DU Xiaoni; HU Jinxia; JIN Wengang; SUN Yanzhong

doi:10.11999/JEIT210720

Volume 44 Issue 10

Oct. 2022

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DU Xiaoni, HU Jinxia, JIN Wengang, SUN Yanzhong. Construction of Two Classes of Minimal Binary Linear Codes[J]. Journal of Electronics & Information Technology, 2022, 44(10): 3643-3649. doi: 10.11999/JEIT210720

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DU Xiaoni, HU Jinxia, JIN Wengang, SUN Yanzhong. Construction of Two Classes of Minimal Binary Linear Codes[J]. Journal of Electronics & Information Technology, 2022, 44(10): 3643-3649. doi: 10.11999/JEIT210720

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Construction of Two Classes of Minimal Binary Linear Codes

doi: 10.11999/JEIT210720

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Funds: The National Natural Science Foundation of China (61772022, 62172337)

Received Date: 2021-07-16
Rev Recd Date: 2022-04-03

Available Online: 2022-04-22

Publish Date: 2022-10-19

Abstract

Abstract

Linear codes play an important role in data storage, information security and secret sharing. Minimal linear codes are the first choice to design secret sharing schemes, so the design of minimal linear codes is one of the important contents of current cryptosystem and coding theory. In this paper, the Walsh spectrum distribution of the selected Boolean functions is studied, and two kinds of minimal linear codes are obtained by using the Walsh spectrum distribution of the functions, then the weight distribution of the codes are determined. The results show that the constructed codes are minimal linear codes that do not satisfy the Ashikhmin-Barg condition, and can be used to design secret sharing schemes with good access structure.
- Boolean functions,
- Walsh transform,
- Binary linear codes

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References(16)

References

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