| Dickson多项式与差集 |
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| 引用本文： | 曹喜望,丘维声.Dickson多项式与差集[J].数学研究及应用,2006,26(2):219-226. |
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| 作者姓名： | 曹喜望 丘维声 |
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| 作者单位： | 1. 南京航空航天大学理学院数学系,江苏,南京,210016
2. 北京大学数学科学学院,北京,100871 |
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| 基金项目： | Acknowledgment The authors would like to express their gratefulness to the referees for valuable comments and suggestions. |
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| 摘 要： | 1998年,Maschietti用超卵形线构造了几个循环差集．R．Evans,H．D．L．Holloman, C．Krattnthaler与Qing Xiang等给出了其对应的二元序列具有良好自相关函数的简单代数证明．在本文中,证明了超卵形线与二对一映射有着紧密的联系,并且推广了Maschietti的结果．
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| 关 键 词： | 循环差集 置换多项式 超卵形线 二对一映射 二元序列 |
| 文章编号： | 1000-341X(2006)02-0219-08 |
| 收稿时间： | 5/9/2004 12:00:00 AM |
| 修稿时间： | 2004年5月9日 |
On Dickson Polynomials and Difference Sets |
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| CAO Xi-wang and QIU Wei-sheng.On Dickson Polynomials and Difference Sets[J].Journal of Mathematical Research with Applications,2006,26(2):219-226. |
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| Authors: | CAO Xi-wang and QIU Wei-sheng |
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| Institution: | School of Math. Sci., Nanjing University of Aeronautics and Astronautics, Jiangsu 210016, China;School of Mathematical Sciences, Peking University, Beijing 100871, China |
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| Abstract: | In 1998, Maschietti constructed several cyclic difference sets from monomial hyperovals. R. Evans, H.D.L. Holloman, C. Krattnthaler and Qing Xiang gave an algebraic proof of the two autocorrelation property of the related binary sequence. In this paper, we show that hyperovals are very closely related to two-to-one maps, and then we proceed to generalize Maschietti's result. |
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| Keywords: | cyclic difference sets permutation polynomials hyperovals two-to-one maps binary sequences |
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