| 对称相关免疫函数的构造与计数 |
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| 引用本文： | 莫骄,温巧燕.对称相关免疫函数的构造与计数[J].北京邮电大学学报,2007,29(1):49-52. |
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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 |
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| 基金项目： | 国家自然科学基金，高等学校博士学科点专项科研项目 |
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| 摘 要： | 指明n元一阶相关免疫对称函数的构造与计数等价于某个方程在二元域上的求解与解的计数，同时指明n元m(m>1)阶相关免疫对称函数的构造也取决于该方程的求解.得到了这个方程的等价方程.通过求解等价方程，提供了高阶相关免疫对称函数的构造方法和一阶相关免疫对称函数的计数方法，并在2种情形下给出了n元一阶相关免疫对称函数的计数下界.
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| 关 键 词： | 对称函数 一阶相关免疫函数 高阶相关免疫函数 等价方程. |
| 文章编号： | 1007-5321（2007）01-0049-04 |
| 收稿时间： | 2006-03-15 |
| 修稿时间： | 2006年3月15日 |
The Construction and Enumeration of Symmetric Correlation Immune Functions |
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| MO Jiao,WEN Qiao-yan.The Construction and Enumeration of Symmetric Correlation Immune Functions[J].Journal of Beijing University of Posts and Telecommunications,2007,29(1):49-52. |
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| Authors: | MO Jiao WEN Qiao-yan |
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| Affiliation: | 1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China |
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| Abstract: | It was claimed that the construction and enumeration of symmetric correlation immune functions with order one was equivalent to the solutions in the binary field and their enumeration for a certain equation. It was also shown that the construction of symmetric correlation immune functions with order rn was also related to the solutions in the binary field of the above equation. The equivalent equation was obtained. By solving the equivalent equation, the methods to construct symmetric corre- lation immune functions with higher order and to enumerate symmetric correlation immune functions with order one were presented. The lower bound of enumeration of symmetric correlation immune functions with order one was also given in two cases. |
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| Keywords: | symmetric functions symmetric correlation immune functions with order one symmetric correlation immune functions with higher order equivalent equation |
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