平衡对称布尔函数的构造与计数

doi:10.13190/jbupt.200605.15.162

北京邮电大学学报 ›› 2006, Vol. 29 ›› Issue (5): 15-18.doi: 10.13190/jbupt.200605.15.162

平衡对称布尔函数的构造与计数

莫骄, 温巧燕

北京邮电大学理学院, 北京 100876

收稿日期:2005-01-01 修回日期:1900-01-01 出版日期:2006-10-30 发布日期:2006-10-30
通讯作者: 莫骄

The Construction and Enumeration of Symmetric Balanced Boolean Functions

MO Jiao , WEN Qiao-yan

School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

Received:2005-01-01 Revised:1900-01-01 Online:2006-10-30 Published:2006-10-30
Contact: MO Jiao

摘要/Abstract

摘要：

据文献[1]，平衡对称布尔函数的构造与计数等价于背包方程的求解与解的计数。本文先求出了当为奇数时这个背包方程的一个解集合以及中所有解的个数，然后给出了这个背包方程存在其它解（即不包含于集合的解）的充分必要条件，同时提供了一种求其它解的方法。最后求出了当（为正整数）时这个背包方程的部分解。

关键词: 平衡函数, 对称函数, 严格雪崩准则, 背包方程。

Abstract:

It is known in conference [1] that the construction and enumeration of symmetric balanced Boolean functions is equivalent to the solution of the knapsack equation and enumeration of the solutions. In this paper, we first find out a set of solutions of this equation when is odd and the number of the elements in is given, then we obtain the necessary and sufficient condition under which there exists other solutions of the equation out of the set .We also show a method for finding out the solutions out of the set . At last some solutions of the equation is given when .

Key words: balanced functions, symmetric functions, strict avalanche criterion, knapsack equation

中图分类号:

TN918.1

莫骄, 温巧燕. 平衡对称布尔函数的构造与计数[J]. 北京邮电大学学报, 2006, 29(5): 15-18.

MO Jiao , WEN Qiao-yan. The Construction and Enumeration of Symmetric Balanced Boolean Functions[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2006, 29(5): 15-18.

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平衡对称布尔函数的构造与计数

The Construction and Enumeration of Symmetric Balanced Boolean Functions

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