关于Bent函数的一些研究

SOME RESEARCH ON BENT FUNCTIONS

包括５个定理．第一个定理提出了一种构造Ｂｅｎｔ函数的新方法，依此可定出大量在实用中很重要的Ｂｅｎｔ函数．第二个定理对２次Ｂｅｎｔ函数进行仿射分类，证明了２次Ｂｅｎｔ函数仅有２类，并定出其每一类中的代表元素．第三个定理指出一类布尔函数不是Ｂｅｎｔ函数．第四个定理研究了Ｂｅｎｔ函数的广义相关免疫性．第五个定理指出了杨义先等的一个错误，说明当ｅ不等于０时。

This paper includes five theorems.The first theorems presents a new method to construct Bent functions.By means of this method,a lot of Bent functions which are very important in practice can be constructed.The second theorem classifies the quadratic Bent functions by the affine classification.We prove that there are only two classes of quadratic Bent functions and give out the represent element of each class.The third theorem presents a class of Boolean functions which isn't Bent function. The fourth theorem presents the extended Correlation-Immune of Bent function.In the fifth theorem,We point out an error in ,demonstrate that the function which is a plus of extended e-Bent function and the nonlinear function is not an extended e-Bent function when e is not equal to zero.