| Umd（3,Fq）的道路图结构及其应用 |
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| 引用本文： | 孔德宝,南基洙. Umd（3,Fq）的道路图结构及其应用[J]. 黑龙江大学自然科学学报, 2012, 29(3): 294-298,302 |
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| 作者姓名： | 孔德宝 南基洙 |
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| 作者单位： | 1. 大连理工大学应用数学系,大连116024;呼伦贝尔学院数学系,呼伦贝尔021008
2. 大连理工大学应用数学系,大连,116024 |
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| 基金项目： | 内蒙古自治区高等学校科学研究项目 |
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| 摘 要： | 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。
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| 关 键 词： | 有限域 道路图 结合方案 |
The path structure of Umd (3, Fq) and its application |
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| KONG De-bao , NAN Ji-zhu. The path structure of Umd (3, Fq) and its application[J]. Journal of Natural Science of Heilongjiang University, 2012, 29(3): 294-298,302 |
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| Authors: | KONG De-bao NAN Ji-zhu |
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| Affiliation: | 1 (1.Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China;2.Department of Mathematics,Hulunbeir University,Hailaer 021008,China) |
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| Abstract: | Let Fq be a finite field with charFq≠2,and Umd(3,Fq) denote the set of nonzero vectors over V3(Fq) where dimV3(Fq)=3.The path structure of vectors α,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 conditions are given.At the same time,use these results to construct some association schemes with many association classes and calculate the corresponding parameters. |
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| Keywords: | finite field path structure of vector association scheme |
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