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

Journal on Communications ›› 2013, Vol. 34 ›› Issue (3): 6-13.doi: 10.3969/j.issn.1000-436x.2013.03.002

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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

Abstract

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

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.

Figures/Tables 1

References 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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