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

作　　者：杨志耀 卓泽朋[1] 崇金凤[1,2] YANG Zhi-yao;ZHUO Ze-peng;CHONG Jin-feng(School of Mathematical Sciences,Huaibei Normal University,Huaibei,Anhui 235000,China;Information College,Huaibei Normal University,Huaibei,Anhui 235000,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000 [2]淮北师范大学信息学院,安徽淮北235000

出　　处：《电子学报》2019年第12期2556-2560,共5页Acta Electronica Sinica

基　　金：国家自然科学基金(No.60573026,No.10101008);安徽省自然科学基金(No.1608085MF143);安徽高校省级自然科学研究重点项目(No.KJ2018A0678);淮北师范大学研究生创新基金(No.ycx201901008)

摘　　要：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.

关 键 词：广义布尔函数 相关函数 BENT函数 平方和指标 广义Walsh-Hadamard变换 

分 类 号：TN918.1[电子电信—通信与信息系统]