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.
出处
《电子学报》
EI
CAS
CSCD
北大核心
2004年第4期654-656,共3页
Acta Electronica Sinica
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
Bent function
multi-dimension Bent function
The families of Bent complementary functions
linear equivalent
reversible symmetrical matrix
