m值逻辑函数的多分块仿射逼近

Multiple Block Affine Approximation of m valued Logical Function

文章定义了ｍ值逻辑函数在Ｄｚｎｍ上的Ｃｈｒｅｓｔｅｎｓｏｎ变换，并考察了这类变换的性质，在此基础上提出了对ｍ值逻辑函数进行多分块仿射逼近的方法，并分析了这种方法的优越性。特别地，重点给出了布尔函数的多分块仿射逼近，并用此方法得到了文献［２］所给出的最大相关子。

This paper defines the Chrestenson transformations of m valued logical functions over a nonempty subset D of z n m and gives some properties of such Chrestenson transformations. Based on it,the methods of multiple block affine approximation of m valued logical functions are proposed. And the superiority of the methods is simultaneously considered. We put a special emphasis on the multiple block affine approximation of Boolean functions. As an application of the results concerned,we obtain the maximum correlators of Boolean functions with the set of all Boolean combinations of a subset of its variables.