2p元2-阶旋转对称弹性布尔函数的构造与计数

doi:10.13190/jbupt.201205.36.duj

北京邮电大学学报 ›› 2012, Vol. 35 ›› Issue (5): 36-40.doi: 10.13190/jbupt.201205.36.duj

2p元2-阶旋转对称弹性布尔函数的构造与计数

杜蛟, 温巧燕, 张劼, 庞善起, 廖鑫

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

收稿日期:2012-03-12 修回日期:2012-05-10 出版日期:2012-10-28 发布日期:2012-07-06
通讯作者: 杜蛟 E-mail:jiaodudj@126.com
作者简介:杜蛟（1978-），男，博士生，Email：jiaodudj@126.com 温巧燕（1959-），女，教授，博士生导师
基金资助:
国家自然科学基金项目（61202434,61272057,61170270,61100203,60903152,61003286,61121061,11171093）；中央高校基本科研业务费专项资金（BUPT2011YB01，BUPT2011RC0505，2011PTB-00-29，2011RCZJ15，2012RC0612）；河南省教育厅自然科学研究计划项目（2011B10010）新乡学院科技创新基金项目

Construction and Counting of Resilient 2-Rotation Symmetric Boolean Functions with 2p Variables

DU Jiao, WEN Qiao-yan, ZHANG Jie, PANG Shan-qi, LIAO Xin

1. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications2. Department of Mathematics and Information Science, Xinxiang University3. School of Science, Beijing University of Posts and Telecommunications4. College of Mathematics and Information Science, Henan Normal University

Received:2012-03-12 Revised:2012-05-10 Online:2012-10-28 Published:2012-07-06
Contact: Jiao DU E-mail:jiaodudj@126.com

摘要/Abstract

摘要：

运用矩阵分析的方法,通过对2p元2-阶旋转对称弹性函数轨道的研究(p≥3,p为素数),给出了其特征矩阵的若干性质.得到了所有的4元2-阶旋转对称布尔函数为弹性函数以及2p元2-阶旋转对称布尔函数为弹性函数的一个充要条件,将这类函数的构造和计数问题转化为3个方程组的求解问题,由此完全决定了2p元2-阶旋转对称弹性函数的构造和这类函数的计数方法.

关键词: 弹性布尔函数, 旋转对称, 特征矩阵, 计数

Abstract:

By using the method of matrix analysis, the orbit of the resilient 2-rotation symmetric Boolean functions with 2p variables is investigated, where p≥3and p is prime. Some properties about characteristic matrix of them are given. A necessary and sufficient condition for 2-rotation symmetric Boolean functions(RSBFs) with 4 or 2p variables being resilient is derived. Construction and counting of this class functions are equivalent to solving three equation systems. Construction and counting of all the resilient 2-RSBFs with 2p variables are determined by this way.

Key words: resilient Boolean function, rotation symmetry, characteristic matrix, counting

中图分类号:

TN918.1

杜蛟, 温巧燕, 张劼, 庞善起, 廖鑫. 2p元2-阶旋转对称弹性布尔函数的构造与计数[J]. 北京邮电大学学报, 2012, 35(5): 36-40.

DU Jiao, WEN Qiao-yan, ZHANG Jie, PANG Shan-qi, LIAO Xin. Construction and Counting of Resilient 2-Rotation Symmetric Boolean Functions with 2p Variables[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2012, 35(5): 36-40.

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2p元2-阶旋转对称弹性布尔函数的构造与计数

Construction and Counting of Resilient 2-Rotation Symmetric Boolean Functions with 2p Variables

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