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.
Abstract
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
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Key words
generalized Boolean functions /
correlation functions /
Bent functions /
sum-of-squares and indicator /
generalized Walsh-Hadamard transform
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中图分类号：
TN918.1
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参考文献
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脚注
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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）
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