Construction of weightwise perfectly balanced Boolean functions with high weightwise nonlinearity

In this paper, we firstly introduce a kind of weightwise almost perfectly balanced Boolean functions. And then, a construction of weightwise perfectly balanced Boolean functions on 2(q+2) variables is given by modifying the support of the weightwise almost perfectly balanced functions, where q is a non-negative 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. (C) 2020 Elsevier B.V. All rights reserved.