一类p值逻辑函数Chrestenson谱的分解式及其应用

A Decomposition Formula of Chrestenson Spectrum of a Class of p valued Logical Functions and Its Application

在考察了一类ｐ（ｐ是素数，ｐ≥２）值逻辑函数Ｃｈｒｅｓｔｅｎｓｏｎ谱的“分解式”的基础上，给出了相关免疫ｐ值逻辑函数的一些新的构造法。

Abstract This paper investigates a decomposition formula of Chrestenson spectrum of a class of p valued logical functions. On the basis of the formula, we give some new methods for construction of correlation immune p valued logical functions. Our main result is the following. Theorem Let f i(x (i) ), h i(x (i) ), x (i) ∈GF n i (p), i=1,…,k, and k≥2, be p valued logical functions, and G(z 1,…,z k),(z 1,…,z k)∈GF k(p), an arbitrary p valued logical function in k indeterminates. Then the second Chrestenson spectrum of the p valued logical function ∑ki=1f i(x (i) )+G(h 1(x (1) ),…,h k(x (k) )) is S (f 1+…+f k+G(h 1,…,h k)) (w (1) ,…,w (k) ) =1p∑p-1r,λ=0u -rλ S (f 1+…+f k-1 +G(h 1,…,h k-1 ,r)) (w (1) ,…,w (k) )·S (f k+λh k) (w (k) ), where w (i) ∈GF n i (p), 1≤i≤k.