Geometric construction of association schemes from non-degenerate quadrics |
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| Authors: | Wang Kaishun Wei Hongzeng |
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| Institution: | (1) Institute of Systems Science, the Academy of Mathematics and Systems Sciences, the Chinese Academy of Sciences, 100080 Beijing, China;(2) Department of Mathematics, Peking University, 100871 Beijing, China;(3) Department of Mathematics, Hebei Normal University, 050091 Shijiazhuang, China |
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| Abstract: | LetF
q
be a finite field withq elements, whereq is a power of an odd prime. In this paper, we assume that δ=0,1 or 2 and consider a projective spacePG(2ν+δ,F
q
), partitioned into an affine spaceAG(2ν+δ,F
q
) of dimension 2ν+δ and a hyperplaneℋ=PG(2ν+δ−1,F
q
) of dimension 2ν+δ−1 at infinity. The points of the hyperplaneℋ are next partitioned into three subsets. A pair of pointsa andb of the affine space is defined to belong to classi if the line
meets the subseti of ℋ. Finally, we derive a family of three-class association schemes, and compute their parameters.
This project is supported by the National Natural Science Foundation of China (No. 19571024). |
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| Keywords: | Association schemes quadrics projective spaces |
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