| 有限域上的逻辑函数与其Chrestenson谱的关系 |
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| 引用本文： | 滕吉红,黄晓英,李世取,曾本胜.有限域上的逻辑函数与其Chrestenson谱的关系[J].数学研究与评论,2005,25(3):504-510. |
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| 作者姓名： | 滕吉红 黄晓英 李世取 曾本胜 |
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| 作者单位： | 解放军信息工程大学信息工程学院信息研究系,河南,郑州,450002 |
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| 摘 要： | 本文首先给出了有限域上逻辑函数的Chrestenson线性谱的新定义(不同于文献1]所给出的),如同Chrestenson循环谱一样,重新定义的Chrestenson线性谱也是有限域Fq到复数域的映射,且证明了它们之间在实质意义下可以相互线性表出;最后我们还用重新定义的Chrestenson线性谱给出了有限域上逻辑函数的反演公式.
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| 关 键 词： | Chrestenson线性谱 Chrestenson循环谱 迹函数 范得蒙矩阵 |
| 文章编号： | 1000-341X(2005)03-0504-07 |
| 收稿时间： | 03 11 2003 12:00AM |
| 修稿时间： | 2003年3月11日 |
Relations between Logical Functions and Their Chrestenson Spectrum over Finite Fields |
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| TENG Ji-hong,HUANG Xiao-ying,LI Shi-qu and ZENG Ben-sheng.Relations between Logical Functions and Their Chrestenson Spectrum over Finite Fields[J].Journal of Mathematical Research and Exposition,2005,25(3):504-510. |
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| Authors: | TENG Ji-hong HUANG Xiao-ying LI Shi-qu and ZENG Ben-sheng |
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| Institution: | Department of Information Research; Information Engineering University; Zhengzhou; China;Department of Information Research; Information Engineering University; Zhengzhou; China;Department of Information Research; Information Engineering University; Zhengzhou; China;Department of Information Research; Information Engineering University; Zhengzhou; China |
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| Abstract: | We firstly redefine the Chrestenson linear spectrum of logical functions over Finite Fields, which was ever offered in 1]. The linear spectrum proposed in this paper, as well as Chrestenson cyclic spectrum, is a mapping from Finite Fields into Complex Fields, so it is reasonable to study the relation between Chrestenson linear spectrum and Chrestenson cyclic spectrum. Finally, we show that any logical functions over finite fields can be deduced by a group of Chrestenson linear spectrum. |
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| Keywords: | Chrestenson linear spectrum Chrestenson cyclic spectrum trace function Vandermonde matrix |
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