代数次数为2的Bent函数的性质及其应用

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+…+x_n-1x_n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k-1个主对角线上元素全为0的n阶可逆对称矩阵M₂…,M_k,使得M₁,M₂…,M_k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.

The Characteristic of Quadratic Bent Functions and Its Applications

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.