Propagation Characteristics of Plateaued Functions

In this paper, we discuss the propagation characteristics of plateaued functions, we give the bounds of autocorrelation coefficient of rth-order plateaued function, present the second-order autocorrelation coefficient of plateaued function, which has some specially properties contrast to autocorrelation coefficient of plateaued functions. Then we demonstrate the number of nonzero autocorrelation coefficient vector of rth-order plateaued function, and demonstrate the values of autocorrelation coefficient of (n-1)th order plateaued functions when n is odd, and (n-2)th order plateaued functions when n is even. Furthermore, we consider the relation between the maximum dimension of linear sup-space and the order of plateaued function, give an especial property of rth-order plateaued function on V_n satisfies the propagation criterion of degree n-1.