Bent函数的一般构造法

A GENERAL CONSTRUCTION OF BENT FUNCTIONS

本文用概率方法给出小项表示的布尔函数谱的性质，据此得到了 Ｂｅｎｔ函数的特征矩阵的等价刻画，原则上给出了 Ｂｅｎｔ函数的一般构造法，并为 Ｂｅｎｔ函数的计数问题提供了一个模型．文中还提出了 Ｂｅｎｔ矩阵的概念，考察了 Ｂｅｎｔ矩阵的性质，并借助 Ｂｅｎｔ矩阵得到由已知 Ｂｅｎｔ函数构造新的

With probability methods,spectrum properties of Boolean functions represented by minor term is studied in this paper.On the basis of this an equivalent description of the characteristic matrix of bent functions is given,then a general method of constructing and counting bent functions is discussed in principle.Bent matrix is introduced for the first time and its properties are examined.At last some methods of constructing new bent functions from known bent functions are presented by bent matrixes.