This paper discusses the structure and properties of spectrum support for plateaued functions.We give the relationship between the set of rth-order plateaued functions’ all nonzero walsh spectrum points and the dimension of linear structure set.Meanwhile

we utilize spectrum index to analyze the autocorrelation properties of both second-order and 4th-order plateaued functions.And the distribution of their autocorrelation coefficient is given.Moreover

we talk about the structure characteristics of rth-order plateaued functions’ spectrum support and zero walsh spectrum points set.We present the relationship among their autocorrelation coefficients and point out the relationship between the spectrum support and the balance property when more rth-order plateaued functions’ spectrum supports are not cross.