A characterization of hadamard designs with SL(2,q) acting transitively |
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Authors: | Wen-Ai Jackson |
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Institution: | (1) Department of Pure Mathematics, University of Adelaide, GPO Box 498, 5001 Adelaide, S.A., Australia |
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Abstract: | Given a hyperoval in a projective plane of even orderq, we can associate a Hadamard 2-design. In the case when is the Desarguesian plane P2,q
,q=2
h
,h>1 and is a regular hyperoval (conic and its nucleus) then a design (q) is obtained. (q) has a point transitive automorphism group isomorphic to PSL(2,q)( SL(2,q)). We classify the designs (q) and P2h–1,2 (the projective space of dimension 2h–1 overF
2) among all the designsH with the same parameters as (q) admitting an automorphism groupGSL(2,q) acting transitively the points ofH. We also describe how all such designsH may be constructed and discuss the problem of when two such designs are isomorphic.This research was supported by Science and Engineering Research Council Grant GR/G 03359. |
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