一类广义布尔函数的相关函数分析

Analysis of Correlation Function of a Class of Generalized Boolean Functions

基于广义布尔函数的理论研究,利用广义Walsh-Hadamard变换、相关函数以及平方和指标,分析了一类广义布尔函数的相关函数关系,得到这类广义布尔函数互相关函数以及自相关函数的关系;基于所得结果,利用自相关函数证明了一类广义Bent函数与Bent函数之间的关系.最后,给出一类广义布尔函数的平方和指标关系.

Based on the theoretical study of the generalized Boolean functions.The correlation functions of a class of generalized Boolean functions are analyzed by using generalized Walsh-Hadamard transform,correlation functions and sum-of-squares and indicator,and the relationship between correlation functions and auto-correlation functions of such generalized Boolean functions are obtained.Based on the results obtained,the relationship between a class of generalized Bent functions and Bent functions is proved by using auto-correlation functions.Finally,the relationship between sum-of-squares and indicator of a class of generalized Boolean functions is given.