二元域上对称循环矩阵的非退化性

The Non-singularity of Symmetric Circulant n×n Matrices over F_2

齐次旋转对称布尔函数与F2n在F2上的一类特殊正规基有着密切的联系,这类正规基的存在性依赖于二元域F2上n×n对称循环矩阵的可逆性.利用有限域上多项式的性质给出了F2上一类n×n对称循环矩阵的行列式计算公式,并由此得到一类特殊的可逆对称循环矩阵.

There is closed relation between homogeneous rotational symmetric Boolean functions and a class of normal bases of F2n over F2.The existence of this kind of normal bases depends on the determinant of symmetric circulant n×n matrices over F2.In the present paper,by using properties of polynomials over finite fields,we give a formula for the determinant of a class of symmetric circulant n×n matrices over F2,and then obtain a special class of nonsingular symmetric circulant matrices over F2.