U_(md)(3,F_q)的道路图结构及其应用

The path structure of U_(md)(3,F_q) and its application

令Fq是特征数不为2的有限域,Umd(3,Fq)表示有限域Fq上3维非零向量组成的集合。在Umd(3,Fq)中研究了不相等的向量α与β道路图的结构。针对d■F2q,0≠d=δ2,d=0不同情形,分别就α与β线性无关和线性相关,讨论了是否存在从α到β的道路;如果存在从α到β的道路,给出α与β的距离及成立的条件。同时利用这些结果构造具有多个结合类的结合方案,而且计算了相应的参数。

Let Fq be a finite field with charFq # 2, and Umd （3, Fq ） denote the set of nonzero vectors over V3 （ Fq ） where dim V3 （ Fq ） = 3. The path structure of vectors or, β ∈ Umd （3, Fq ）, and α ≠β is studied. For several cases d F2q, 0 # d = δ2 and d = 0, whether there is a path structure of vector from α to β is discussed, respectively, when α and β are linearly independent and linear dependent. If so, then the distance between α and β and existing con- ditions are given. At the same time, use these results to construct some association schemes with many association classes and calculate the corresponding parameters.