| 偶数元平衡对称布尔函数的构造与计数 |
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| 引用本文： | 莫骄,温巧燕. 偶数元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(6): 25-27 |
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| 作者姓名： | 莫骄 温巧燕 |
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| 作者单位： | 北京邮电大学,理学院,北京,100876;北京邮电大学,理学院,北京,100876 |
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| 基金项目： | 国家自然科学基金项目（60373059）;教育部博士点基金项目（20040013007） |
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| 摘 要： | 平衡对称布尔函数的构造与计数等价于二元域上某个含有n个变量的背包方程的求解与解的计数，并且当n为偶数时，该背包方程存在2组平凡解。给出了当 为偶数时，这个背包方程有非平凡解的充分必要条件；提供了1种求非平凡解的方法；求出了当 和 （ 为正整数）时，这个背包方程的非平凡解。
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| 关 键 词： | 平衡函数 对称函数 背包方程 非平凡解 |
| 文章编号： | 1007-5321（2006）06-0025-03 |
| 收稿时间： | 2005-11-28 |
| 修稿时间： | 2005-11-28 |
The Construction and Enumeration of Symmetric Balanced Boolean Functions with Even Number of Variables |
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| MO Jiao,WEN Qiao-yan. The Construction and Enumeration of Symmetric Balanced Boolean Functions with Even Number of Variables[J]. Journal of Beijing University of Posts and Telecommunications, 2006, 29(6): 25-27 |
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| Authors: | MO Jiao WEN Qiao-yan |
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| Affiliation: | School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China |
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| Abstract: | The construction and enumeration of symmetric balanced Boolean functions is equivalent to the solution and enumeration of the solution of one knapsack equation with n variables in the binary field. There exist two trivial solutions of this knapsack equation when is even. The necessary and sufficient condition under which there exist non-trivlal solutions of this knapsack equation was given when is even. A method for finding out the non-trivial solutions was also shown. Some non-trivial solutions of this knapsack equation were found out when and. |
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| Keywords: | balanced functions symmetric functions knapsack equation non-trivial solutions |
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