The Count Related To Immune Function And Features

This dissertation is on the enumeration and specific properties study such as non-degeneration and linear structure of functions with correlation immunity. The main results are as follows:1. The paper revises the enumeration formula of n-variable Boolean functions with correlation-immunity for the case of weight 6(or 2n -6) in bibliography [9], thengives the exact number for the case of weight 8(or 2n-8) and 10(or 2n-10); furthermore, it provides the exact number of 5-variable CIB functions for the first time.2. It gives a detailed study on the non-degenerated Boolean functions with correlation immunity and presents a better bound for such functions. It provides the analytic equation of G(K) in bibliography [5]; By analyzing linear structures of CIB, it proves that the concept of linear structure and degeneration of CIB for the case of weight 4k+2 are equivalent; provides a sufficient condition on which CIB functions are non-degenerated for the case of weight 4k; Based on these results, a method of constructing non-degenerated CIB is given.3. It discusses the non-degeneration of higher-order CIB functions. It gives an analysis of the methods of constructing orthogonal matrixes in bibliography [5] and [18], proves that the functions obtained using these methods are all degenerated; gives a conclusion that all the 2-order functions are degenerated for the case of weight 8; presents a simpler proof for the theorem 'all the 2-order CIB functions are non-degenerated for the case of weight 8k+4'in bibliography [5]; provides an example of non-degenerated balanced 2-order CIB for the first time.4. It characterizes the linear structure of m-valued logic functions using their characteristic groups, gives a method to look for the linear structure of such functions; moreover, points out an error in bibliography [8].