偶特征有限正交空间中的几个计数公式及应用

Some Anzahl Formulas in Finite Orthogonal Spaces of Charcteristic Even and Its Applications

设Fq(n)是Fq上的n维正交空间,设P是任一个给定的m维全奇异子空间.计算了F(qn)中满足dim(P∩Q)=i的r维全奇异子空间Q的个数,给出了用子空间构作认证码的例子.

Let Fq^（n） be the n-dimensional orthogonal space over the finite Fq and let P be the m-dimensional totally singularity subspace in Fq^（n）. The number of r-dimensional totally singularity subspaces Q such that dim（P ∩ Q）= i is computed. Furthermore,som authentication codes are constructed using the subspaces in Fq^（n） .