Mathematics

CLC number: O29

The Walsh Transform of a Class of Boolean Functions

¹ School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, Anhui, China
² School of Cyber Science, University of Science and Technology of China, Hefei 230027, Anhui, China
³ School of Computer Engineering, Bengbu University, Bengbu 233030, Anhui, China

† To whom correspondence should be addressed. E-mail: cglbox@sina.com

Received: 4 August 2021

Abstract

The Walsh transform is an important tool to investigate cryptographic properties of Boolean functions. This paper is devoted to study the Walsh transform of a class of Boolean functions defined as $g(x)=f(x){\text{Tr}}_1^n(x)+h(x){\text{Tr}}_1^n(\delta x)$, by making use of the known conclusions of Walsh transform and the properties of trace function, and the conclusion is obtained by generalizing an existing result.