A new construction of weightwise perfectly balanced Boolean functions

In this paper, we first introduce a class of quartic Boolean functions. And then, the construction of weightwise perfectly balanced Boolean functions on $ 2^m $ variables are given by modifying the support of the quartic functions, where $ m $ is a positive integer. The algebraic degree, the weightwise nonlinearity, and the algebraic immunity of the newly constructed weightwise perfectly balanced functions are discussed at the end of this paper.