Several new classes of Boolean functions with few Walsh transform values

In this paper, several new classes of Boolean functions with few Walsh transform values, including bent, semi-bent and five-valued functions, are obtained by adding the product of two or three linear functions to some known bent functions.Numerical results show that the proposed class contains cubic bent functions that are affinely inequivalent to all known quadratic ones. Meanwhile, we determine the distribution of the Walsh spectrum of five-valued functions constructed in this paper.