Several new classes of (balanced) Boolean functions with few Walsh transform values

Three classes of (balanced) Boolean functions with few Walsh transform values derived from bent functions, Gold functions and the product of linearized polynomials are obtained in this paper. Further, the value distributions of their Walsh transform are also determined by virtue of the property of bent functions, the Walsh transform property of Gold functions and the \begin{document}$ k $\end{document} -tuple balance property of trace functions respectively.