引用本文: | 李平,周悦,李超.一类完全非线性函数的证明与计数[J].国防科技大学学报,2010,32(3):144-148.[点击复制] |
LI Ping,ZHOU Yue,LI Chao.Proof and Count of a Family of Perfect Nonlinear Functions[J].Journal of National University of Defense Technology,2010,32(3):144-148[点击复制] |
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一类完全非线性函数的证明与计数 |
李平, 周悦, 李超 |
(国防科技大学 理学院,湖南 长沙 410073)
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摘要: |
Helleseth等最近给出了一类二项式形式的完全非线性函数,这是至今为止所发现的第一类由两个互不等价的单项式组成的二项式形式的完全非线性函数。本文利用Frobinus自同构将其变形为一个新的二项式,给出了其完全非线性的简洁证明,指出了这类函数与 x2是等价的,最后讨论了该类完全非线性函数的计数性质。 |
关键词: 完全非线性函数 扩展仿射等价 计数 |
DOI: |
投稿日期:2009-09-10 |
基金项目:国家自然科学基金资助项目(60803156);信息安全国家重点实验室开放基金资助项目(01-07) |
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Proof and Count of a Family of Perfect Nonlinear Functions |
LI Ping, ZHOU Yue, LI Chao |
(College of Science, National Univ. of Defense Technology,Changsha 410073, China)
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Abstract: |
A new class of perfect nonlinear binomials was just found by Helleseth et al, which are the first perfect nonlinear binomials composed with two inequivalent monomials. We transformed the class of perfect nonlinear binomials to another form, and gave a concise proof for their perfect nonlinearness. It shows that this family of binomials is equivalent to . Furthermore, the calculation of the count of this family of functions is presented as well. |
Keywords: perfect nonlinear functions extended affine equivalence counting |
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