On small minimal blocking sets of Q(4,q), q odd


We consider the classical generalized quadrangle Q(4,q). A blocking set is a set B of points of Q(4,q) such that every line of Q(4,q) meets K in at least one point. It is known that small minimal blocking sets of Q(4,q) do not exist when q=2h, while when q is odd, very few is known. Using an algebraic description of W(3,q), the point-line dual of Q(4,q), we are able to compute intersection numbers of small blocking sets of Q(4,q) with hyperplanes of PG(4,q). It turns out that these intersection numbers are strong enough to exclude the existence of minimal blocking sets of size q2+2 of Q(4,q), for q an odd prime. We will discuss the algebraic description, the computation of the intersection numbers and the geometric part of the proof of the non-existence of minimal blocking sets of size q2+2 for q odd.

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