特征为2的有限域上对称矩阵方程解的计数公式及q超几何级数表达  

The Number of Solutions to the Symmetric Matrix Equation over a Finite Field of Ch_o=2 and Representation of Its q-hypergeometric Series

作　　者：魏鸿增[1] 张谊宾[1] 王崇寿[2] 

机构地区：[1]河北师范大学,石家庄050091 [2]北京建工学院,北京100084

出　　处：《数学学报（中文版）》1999年第1期23-34,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金;河北省教委科研项目

摘　　要：设Fq是有q＝2t个元的有限域.本文利用Fq上奇异辛几何和奇异伪辛几何理论，给出当A，C是Fq上对称矩阵时，Fq上适合XAXT＝C的解存在的充要条件以及秩k的解X和解X的个数的明显公式，并且用q超几何级数简化表达解数公式．Let Fq be a finite field with q=2t elements. In this paper, using singular symplectic and singular pseudo-symplactic geometry over Fq, we have given the sufficient and necessary condition of there exists solutions and the number of solutions X of rank k and solutions X to the equation XAXT=B over Fq. when A and B are symmetric matrices. Finally. we have obtained simple representations of enumerational formulas by q-hypergeometric series.

关 键 词：对称矩阵方程 Q超几何级数 有限域 计数公式 解 

分 类 号：O151.21[理学—数学]