共查询到19条相似文献,搜索用时 101 毫秒
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m值逻辑函数的谱分解式及广义Bent函数的递归构造 总被引:1,自引:0,他引:1
本文用概率方法得到m值逻辑函数Chrestenson循环谱的分解式,据此考察了m值广义Bent函数一些新的性质,给出了递归构造m(m≠2mod4)值广义Bent函数的一般方法. 相似文献
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本文将基本2-群中拟Bent函数的概念推广到一般的有限Abel群中,统一了目前几乎所有的Bent函数概念,完全刻画了一类拟Bent函数和Bent函数的本质联系,给出了几种拟Bent函数的构造方法,拟Bent函数和相对差集的一种关系以及一种用拟Bent函数构造Bent函数的方法.最后,利用Galois环和组合集,找到一类拟Bent函数. 相似文献
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Rothaus在其文章《On Bent Functions》中指出代数次数为3的6元Bent函数只有3个等价类.本文则推导出代数次数为3的6元Bent函数各等价类中函数的具体结构形式,并由此给出了以任意一个代数次数是3的6元Bent函数为分量的多维Bent函数的构造法. 相似文献
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《数学的实践与认识》2019,(22)
提出解析函数的弱从属概念,证明弱从属的一些基本性质,建立弱从属原理,推广经典从属关系基本理论;最后,利用具体例子给出了利用"弱从属"构造和研究广义解析函数类的一种方法,所得结果推广Janowski函数和一致凸函数基本性质,并得到一些有趣的新结果. 相似文献
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周建锋 《数学的实践与认识》2014,(3)
研究由三元双正交插值尺度函数构造对应的双正交小波滤波器的矩阵扩充问题.当给定的一对三元双正交尺度函数中有一个为插值函数时,利用提升思想与矩阵多相分解方法,给出一类三元双正交小波滤波器的显示构造公式和一个计算实例.讨论了三元双正交小波包的的性质. 相似文献
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获得了在Sl^(s)[a,b]函数类中具有对称与中心对称性质的矩阵值两边留数插值问题的可解性条件。给出该问题所有解的一个线性分式变换表达形式.所用的方法是构造相同的矩阵函数作为线性分式变换的系数矩阵。 相似文献
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This paper discusses a kind of bent functions that have some symmetric properties about some variables. Section 2 mainly discusses the bent functions symmetric about some two variables and gives the necessary and sufficient condition for these functions. Section 3 gives algebraic expressions of some bent functions. 相似文献
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In this article a technique for constructing p-ary bent functions from near-bent functions is presented. This technique is then used to obtain both weakly regular and non-weakly regular bent functions. In particular we present the first known infinite class of non-weakly regular bent functions. 相似文献
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A class of bent functions which contains bent functions with various properties like regular, weakly regular and not weakly regular bent functions in even and in odd dimension, is analyzed. It is shown that this class includes the Maiorana–McFarland class as a special case. Known classes and examples of bent functions in odd characteristic are examined for their relation to this class. In the second part, normality for bent functions in odd characteristic is analyzed. It turns out that differently to Boolean bent functions, many – also quadratic – bent functions in odd characteristic and even dimension are not normal. It is shown that regular Coulter–Matthews bent functions are normal. 相似文献
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In this presentation, a technique for constructing bent functions from plateaued functions is introduced and analyzed. This generalizes earlier techniques for constructing bent from near-bent functions. Using this construction, we obtain a big variety of inequivalent bent functions, some weakly regular and some non-weakly regular. Classes of bent functions having some additional properties that enable the construction of strongly regular graphs are formed, and explicit expressions for bent functions with maximal degree are presented. 相似文献
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广义部分Bent函数和广义Bent函数的关系 总被引:5,自引:0,他引:5
Bent函数是一类特殊的布尔函数,因其非线性性和稳定性在密码学和通信等领域有很重要的应用,但它们数量少,不平衡且无相关免疫性,为了弥补Bent函数的不足,Claud Carlet提出了部分Bent函数的概念,部分Bent函数是包含Bent函数的更大的函数类,后来,人们又将这两种函数概念先后都拓广到了环zm^n(m为正整数)上,分别被称为zm^n上的广义Bent函数和广义部分Bent函数,本文利用zp^n(p为素数)上广义部分Bent函数的Chrestenson循环谱特征讨论了zp^n上的广义部分Bent函数和广义Bent函数之间的关系,给出了这两种函数之间的函数关系式和谱值关系式。 相似文献
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本文利用分圆域中的素理想分解特性和一些特殊的不定方程的解性质,得到一些特殊类型的广义Bent函数的不存在性结果。 相似文献
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On the ranks of bent functions 总被引:2,自引:0,他引:2
The rank of a bent function is the 2-rank of the associated symmetric 2-design. In this paper, it is shown that it is an invariant under the equivalence relation among bent functions. Some upper and lower bounds of ranks of general bent functions, Maiorana–McFarland bent functions and Desarguesian partial spread bent functions are given. As a consequence, it is proved that almost every Desarguesian partial spread bent function is not equivalent to any Maiorana–McFarland bent function. 相似文献
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The question if there exist nonnormal bent functions was an open question for several years. A Boolean function in n variables is called normal if there exists an affine subspace of dimension n/2 on which the function is constant. In this paper we give the first nonnormal bent function and even an example for a nonweakly normal bent function. These examples belong to a class of bent functions found in [J.F. Dillon, H. Dobbertin, New cyclic difference sets with Singer parameters, in: Finite Fields and Applications, to appear], namely the Kasami functions. We furthermore give a construction which extends these examples to higher dimensions. Additionally, we present a very efficient algorithm that was used to verify the nonnormality of these functions. 相似文献