Spectral analysis of high order correlation immune functions

Abstract

We consider F/sub 2//sup n/, the vector space of n-tuples of elements from F/sub 2/. An n-variable Boolean function is a map from F/sub 2//sup n/ into F/sub 2/. The weight of a vector x is the number of ones in x and is denoted by |x|. The weight wt(f) of a function f on F/sub 2//sup n/ is the number of vectors x on F/sub 2//sup n/ such that f(x)=1. A function f is said to be balance if wt(f)=wt(f/spl oplus/1)=2/sup n-1/. A subfunction of the Boolean function f is a function f/spl acute/ obtained by substituting some constants for some variables in f.