旋转对称布尔函数线性结构的2个公开问题

doi:10.3969/j.issn.1000-436x.2013.03.022

通信学报 ›› 2013, Vol. 34 ›› Issue (3): 171-174.doi: 10.3969/j.issn.1000-436x.2013.03.022

旋转对称布尔函数线性结构的2个公开问题

赵亚群^1,²,李旭¹

¹ 信息工程大学四院，河南郑州 450002
² 信息工程大学数学工程与先进计算国家重点实验室，河南郑州 450002

出版日期:2013-03-25 发布日期:2017-07-20
基金资助:
国家自然科学基金资助项目

Two open problems about the liner structure of rotation symmetric Boolean functions

Ya-qun ZHAO^1,²,Xu LI¹

¹ The Fourth Institute, Information Engineering University, Zhengzhou 450002, China
² State Key Laboratory of Mathematical Engineering and Advanced Computing, Information Engineering University, Zhengzhou 450002, China

Online:2013-03-25 Published:2017-07-20
Supported by:
The National Natural Science Foundation of China

摘要/Abstract

摘要：

证明了代数次数为n?1的偶变元平衡旋转对称布尔函数不存在非零线性结构这个公开问题，给出了代数次数为n?2的奇变元旋转对称布尔函数不存在非零线性结构这个公开问题成立的充分条件和不成立的必要条件。

关键词: 布尔函数, 旋转对称, 线性结构, 代数次数

Abstract:

One open problem that the balanced rotation symmetric Boolean functions with degree n? 1 on even number of variables have no non-zero linear structure was proved. A sufficient and a necessary condition were respectively given when another open problem that the rotation symmetric ean functions with degree n? 2 on odd number of va-riables have no non-zero linear structure succeed or not.

Key words: Boolean functions, rotation symmetric, linear structure, algebraic degree

赵亚群,李旭. 旋转对称布尔函数线性结构的2个公开问题[J]. 通信学报, 2013, 34(3): 171-174.

Ya-qun ZHAO,Xu LI. Two open problems about the liner structure of rotation symmetric Boolean functions[J]. Journal on Communications, 2013, 34(3): 171-174.

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旋转对称布尔函数线性结构的2个公开问题

Two open problems about the liner structure of rotation symmetric Boolean functions

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