Several new classes of (balanced) Boolean functions with few Walsh transform values

Tingting Pang; Nian Li; Li Zhang; Xiangyong Zeng

doi:10.3934/amc.2020095

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2021, Volume 15, Issue 4: 757-775. Doi: 10.3934/amc.2020095

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Several new classes of (balanced) Boolean functions with few Walsh transform values

1.
Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China
2.
Wuhan Maritime Communication Research Institute, Wuhan 430079, China

^* Corresponding author: Nian Li
^* Corresponding author: Nian Li

Received: February 2020

Revised: April 2020

Early access: July 2020

Published: November 2021

This work was supported by the National Natural Science Foundation of China (Nos. 61702166, 61761166010) and Major Technological Innovation Special Project of Hubei Province (No. 2019ACA144)

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Abstract

Three classes of (balanced) Boolean functions with few Walsh transform values derived from bent functions, Gold functions and the product of linearized polynomials are obtained in this paper. Further, the value distributions of their Walsh transform are also determined by virtue of the property of bent functions, the Walsh transform property of Gold functions and the $k$ -tuple balance property of trace functions respectively.

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Mathematics Subject Classification: Primary: 94A60, 11T23; Secondary: 06E30.

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