代数次数为2的Bent函数的性质及其应用  

The Characteristic of Quadratic Bent Functions and Its Applications

作　　者：张文英[1] 李世取[1] 

机构地区：[1]郑州信息工程学院信息研究系,河南郑州450002

出　　处：《电子学报》2004年第4期654-656,共3页Acta Electronica Sinica

摘　　要：本文证明了任意代数次数为2的n元Bent函数都与形式为x1x2+x3x4+…+xn-1xn的Bent函数线性等价;给出了以任意已知代数次数为2的n元Bent函数为分量的多维Bent函数的构造法;利用本文所给的方法,对任一主对角线上元素全为0的n阶可逆对称矩阵M1,都可以构造造k-1个主对角线上元素全为0的n阶可逆对称矩阵M2…,Mk,使得M1,M2…,Mk的任意非零线性组合仍是主对角线上元素全为0的阶可逆对称矩阵.This paper gives a proof that all Bent functions of degree 2 are linearly equivalent each other and presents a method for constructing multi-dimension Bent functions when one output variable is of degree 2. For a given reversible symmetrical matrix with the elements of its diagonal is 0, it provides a method for constructing k - 1' s reversible symmetrical matrixes,such that every non-zero linear combination of these k's matrixes is also a reversible symmetrical matrix.

关 键 词：BENT函数 多维Bent函数 Bent互补函数族 线性等价 可逆对称矩阵 

分 类 号：TN918.1[电子电信—通信与信息系统]