A note on generalization of bent boolean functions
Bimal Mandal, Aditi Kar Gangopadhyay · Advances in Mathematics of Communications · 2020
Suppose that \begin{document}$ \mu_p $\end{document} is a probability measure defined on the input space of Boolean functions. We consider a generalization of Walsh–Hadamard transform on Boolean functions to \begin{document}$ \mu_p $\end{document} -Walsh–Hadamard transforms. In this paper, first, we derive the properties of \begin{document}$ \mu_p $\end{document} -Walsh–Hadamard transformation for some classes of Boolean functions and specify a class of nonsingular affine transformations that preserve the \begin{document}$ \mu_p $\end{document} -bent property. We further derive the results on \begin{document}$ \mu_p $\end{document} -Walsh–Hadamard transform of concatenation of Boolean functions and provide some secondary constructions of \begin{document}$ \mu_p $\end{document} -bent functions. Finally, we discuss the \begin{document}$ \mu_p $\end{document} -bentness for Maiorana–McFarland class of bent functions.