摘要
利用矩阵的permanent的性质,构造一个生成函数,用于计算有限域上一类特殊方程的解数.而针对有限域上的某些特殊子群,利用矩阵的permanent表示该方程的解数,然后再利用Hermite矩阵的性质以及Gauss和估计复矩阵的奇异值,从而对该矩阵permanent值进行估计,最终得到该方程解数的一个估计.
By using the properties of the permanent of a matrix,a generating function was constructed to calculate the number of solutions of a kind of equation over finite field.For some special subgroups over finite field,there are some matrices whose permanents are used to represent the number of solutions of the equations.With the properties of Hermitian matrix and Gauss sum,the singular values of these matrices can be evaluated so as to estimate the permanents of these complex matrices.Finally the number of solutions of this equation is estimated.
作者
高巍
张起帆
GAO Wei;ZHANG Qi-fan(School of Mathematics,Sichuan University,Chengdu 610064,P.R.C.)
出处
《西南民族大学学报（自然科学版）》
CAS
2019年第6期625-630,共6页
Journal of Southwest Minzu University(Natural Science Edition)
基金
国防应用项目(0020105501055)
