Analysis of Correlation Function of a Class of Generalized Boolean Functions

YANG Zhi-yao; ZHUO Ze-peng; CHONG Jin-feng

doi:10.3969/j.issn.0372-2112.2019.12.014

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Analysis of Correlation Function of a Class of Generalized Boolean Functions

更新时间：2025-07-16

- Analysis of Correlation Function of a Class of Generalized Boolean Functions
- Acta Electronica Sinica Vol. 47, Issue 12, Pages: 2556-2560(2019)
- 作者机构：
  
  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
  3. 淮北师范大学数学科学学院,安徽,淮北,235000
  4. 淮北师范大学信息学院,安徽,淮北,235000
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2019.12.014
  CLC： TN918.1
- Published Online：25 December 2019，
  
  Published：2019
- 稿件说明：
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YANG Zhi-yao, ZHUO Ze-peng, CHONG Jin-feng. Analysis of Correlation Function of a Class of Generalized Boolean Functions[J]. Acta Electronica Sinica, 2019, 47(12): 2556-2560.
DOI：

YANG Zhi-yao, ZHUO Ze-peng, CHONG Jin-feng. Analysis of Correlation Function of a Class of Generalized Boolean Functions[J]. Acta Electronica Sinica, 2019, 47(12): 2556-2560. DOI： 10.3969/j.issn.0372-2112.2019.12.014.

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.

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.

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