素数元旋转对称弹性布尔函数的构造与计数

doi:10.3969/j.issn.1000-436x.2013.03.002

通信学报 ›› 2013, Vol. 34 ›› Issue (3): 6-13.doi: 10.3969/j.issn.1000-436x.2013.03.002

素数元旋转对称弹性布尔函数的构造与计数

杜蛟^1,²,温巧燕¹,张劼³,庞善起⁴

¹ 北京邮电大学网络与交换技术国家重点实验室，北京 100876
² 新乡学院数学与信息科学系，河南新乡 453003
³ 北京邮电大学理学院，北京 100876
⁴ 河南师范大学数学与信息科学学院，河南新乡 453007

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;国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;中央高校基本科研业务费专项基金资助项目;中央高校基本科研业务费专项基金资助项目;中央高校基本科研业务费专项基金资助项目;中央高校基本科研业务费专项基金资助项目;中央高校基本科研业务费专项基金资助项目;河南省教育厅自然科学研究计划基金资助项目;2010年新乡学院科技创新基金资助项目

Construction and count of resilient rotation symmetric Boolean functions with prime number variables

Jiao DU^1,²,Qiao-yan WEN¹,Jie ZHANG³,Shan-qi PANG⁴

¹ State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
² Department of Mathematics and Information Science, Xinxiang University,Xinxiang 453003, China
³ School of Science, Beijing University of Posts and Telecommunications,Beijing 100876, China
⁴ College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

Online:2013-03-25 Published:2017-07-20
Supported by:
The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;The Fundamental Research Funds for the Central Universities;The Fundamental Research Funds for the Central Universities;The Fundamental Research Funds for the Central Universities;The Fundamental Research Funds for the Central Universities;The Fundamental Research Funds for the Central Universities;The Natural Science Research Program of the Education Department of Henan Prov-ince;The Science and Technology Innovat ion of Xinxiang University 2010

摘要/Abstract

摘要：

通过对素数元旋转对称弹性布尔函数特征矩阵的研究，给出了其特征矩阵的若干性质，得到了素数元旋转对称布尔函数为弹性函数的一个充要条件，由此完全决定了旋转对称弹性函数的构造以及这类函数的精确计数公式，最后还给出了所有的三元、五元、七元旋转对称弹性布尔函数的构造方案与精确计数。

关键词: 布尔函数, 特征矩阵, 相关免疫, 代数免疫

Abstract:

The characteristic matrix of the resilient rotation symmetric Boolean functions(RSBF) with prime number va-riables were explored. Some properties about character ic matrix of them were given. A necessary and sufficient condi-tion on the construction of resilient RSBF with prime number variables was derived. So construction and count formula of all the resilient RSBF with prime number variables were determined by this way. At last, all the resilient RSBF with 3, 5 or 7 variables were given.

Key words: Boolean functions, characteristic matrix, correlation immune, algebraic immunity

杜蛟,温巧燕,张劼,庞善起. 素数元旋转对称弹性布尔函数的构造与计数[J]. 通信学报, 2013, 34(3): 6-13.

Jiao DU,Qiao-yan WEN,Jie ZHANG,Shan-qi PANG. Construction and count of resilient rotation symmetric Boolean functions with prime number variables[J]. Journal on Communications, 2013, 34(3): 6-13.

图/表 1

参考文献 22

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素数元旋转对称弹性布尔函数的构造与计数

Construction and count of resilient rotation symmetric Boolean functions with prime number variables

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参考文献 22

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组号	n₁	n₂	n₃	n₄	n₅	n₆	函数个数T_j
1	0	0	4	5	0	0	5
2	0	0	5	3	1	0	30
3	0	1	3	4	1	0	450
4	0	1	4	2	2	0	450
5	0	1	4	3	0	1	150
6	0	1	5	0	3	0	3
7	0	1	5	1	1	1	45
8	0	2	1	5	1	0	45
9	0	2	2	3	2	0	900
10	0	2	2	4	0	1	150
11	0	2	3	1	3	0	150
12	0	2	3	2	1	1	900
13	0	2	4	0	2	1	45
14	0	3	0	4	2	0	15
15	0	3	0	5	0	1	1
16	0	3	1	2	3	0	50
17	0	3	1	3	1	1	150
18	0	3	2	1	2	1	150
19	1	0	2	5	1	0	30
20	1	0	3	3	2	0	300
21	1	0	3	4	0	1	50
22	1	0	4	1	3	0	25
23	1	0	4	2	1	1	150
24	1	0	5	0	2	1	3
25	1	1	1	4	2	0	225
26	1	1	1	5	0	1	15
27	1	1	2	2	3	0	300
28	1	1	2	3	1	1	900
29	1	1	3	1	2	1	450
30	1	2	0	3	3	0	30
31	1	2	0	4	1	1	45
32	1	2	1	2	2	1	450
33	1	2	2	0	3	1	30
34	1	3	0	1	3	1	5

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