Reconstructing a generalized quadrangle with a hemisystem from a $4-$ class association scheme

preprint2022arXivOpen access

In 2013, van Dam, Martin and Muzychuk constructed a cometric $Q-$ antipodal $4-$ class association scheme from a GQ of order $(t^2,t)$ , $t$ odd, which have a hemisystem. In this paper we characterize this scheme by its Krein array. The techniques which are used involve the triple intersection numbers introduced by Coolsaet and Jurišić.

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Reconstructing a generalized quadrangle with a hemisystem from a $4-$ class association scheme

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Reconstructing a generalized quadrangle with a hemisystem from a 4−4-4−class association scheme

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Reconstructing a generalized quadrangle with a hemisystem from a $4-$ class association scheme