Three new infinite families of bent functions

Abstract

Bent functions are maximally nonlinear Boolean functionswith an even number of variables. They are closely related to someinteresting combinatorial objects and also have importantapplications in coding, cryptography and sequence design. In thispaper, we firstly give a necessary and sufficient condition for a type of Boolean functions, which obtained by adding the product of finitely many linear functions to given bent functions, to be bent.In the case that these known bent functions are chosen to be Kasamifunctions, Gold-like functions and functions with Niho exponents,respectively, three new explicit infinite families of bent functionsare obtained. Computer experiments show that the proposed familesalso contain such bent functions attaining optimal algebraic degree.