Constructions of Boolean functions with five-valued Walsh spectra and their applications

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences Pub Date : 2023-01-01 DOI:10.1587/transfun.2023eap1064

Yingzhong ZHANG, Xiaoni DU, Wengang JIN, Xingbin QIAO

引用次数: 0

Abstract

Boolean functions with a few Walsh spectral values have important applications in sequence ciphers and coding theory. In this paper, we first construct a class of Boolean functions with at most five-valued Walsh spectra by using the secondary construction of Boolean functions, in particular, plateaued functions are included. Then, we construct three classes of Boolean functions with five-valued Walsh spectra using Kasami functions and investigate the Walsh spectrum distributions of the new functions. Finally, three classes of minimal linear codes with five-weights are obtained, which can be used to design secret sharing scheme with good access structures.

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五值Walsh谱布尔函数的构造及其应用

具有少量沃尔什谱值的布尔函数在序列密码和编码理论中有着重要的应用。本文首先利用布尔函数的二次构造构造了一类最多有五值Walsh谱的布尔函数，其中包括了平台函数。然后，利用Kasami函数构造了3类具有5值Walsh谱的布尔函数，并研究了新函数的Walsh谱分布。最后，得到了3类五权最小线性码，可用于设计具有良好访问结构的秘密共享方案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences 工程技术-工程：电子与电气

CiteScore

1.10

自引率

20.00%

发文量

137

审稿时长

3.9 months

期刊介绍： Includes reports on research, developments, and examinations performed by the Society''s members for the specific fields shown in the category list such as detailed below, the contents of which may advance the development of science and industry: (1) Reports on new theories, experiments with new contents, or extensions of and supplements to conventional theories and experiments. (2) Reports on development of measurement technology and various applied technologies. (3) Reports on the planning, design, manufacture, testing, or operation of facilities, machinery, parts, materials, etc. (4) Presentation of new methods, suggestion of new angles, ideas, systematization, software, or any new facts regarding the above.