The sum of modules of Walsh coefficients of Boolean functions

Abstract

AbstractWe obtain achievable lower and upper bounds for the sums of modules of Walsh coefficients of Boolean functions of nvariables. An average value of such sums in the class of all Boolean functions of n variables and in its subclass consisting of all balanced functions is evaluated. We present some classes of nonlinear balanced functions whose sums of modules of Walsh coefficients are close to the obtained lower and upper bounds