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关于正形置换多项式的注记   总被引:5,自引:1,他引:4  
n为正整数,m为大于1的正整数,本文证明了当n≡0,1(mod m)时,F2^n上不存在2^m-1次正形置换多项式,并给出了该结果的几个推论:F2^n上不存在次数为3的正形置换多项式;n〉2时,F2^n上的4次正形置换多项式都是仿射多项式.  相似文献   
2.
线性结构是度量密码函数安全性的一个重要指标.基于有限域理论,本文从多项式的角度分析了16元域上正形置换的线性结构,得到了该域上所有正形置换多项式的线性结构集维数,其中次数为11和13的所有正形置换多项式以及次数为10和12的部分正形置换多项式没有非零线性结构.  相似文献   
3.
Planar functions were introduced by Dembowski and Ostrom [4] to describe projective planes possessing a collineation group with particular properties. Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes. This resolves in the negative a question posed in [4]. These planar functions define at least one such affine plane of order 3e for every e 4 and their projective closures are of Lenz-Barlotti type II. All previously known planes of type II are obtained by derivation or lifting. At least when e is odd, the planes described here cannot be obtained in this manner.  相似文献   
4.
最近,Dillon和Dobbertin证明了在有限域Fq(q=2m)的乘法群中,多项式(x+1)d+xd+1(其中d=22k-2k+1)的像集是一个新的具有Singer参数的循环差集.利用有限域上的Fourier分析,本文证明了在有限域Fq(q=2m)的乘法群中,一些用Dickson多项式构造的集合是具有Singer参数的循环差集.  相似文献   
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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.  相似文献   
6.
Permutation polynomials have been an interesting subject of study for a long time and have applications in many areas of mathematics and engineering. However, only a small number of specific classes of permutation polynomials are known so far. In this paper, six classes of linearized permutation polynomials and six classes of nonlinearized permutation polynomials over are presented. These polynomials have simple shapes, and they are related to planar functions. This work was supported by Australian Research Council (Grant No. DP0558773), National Natural Science Foundation of China (Grant No. 10571180) and the Research Grants Council of the Hong Kong Special Administrative Region of China (Grant No. 612405)  相似文献   
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