Patrick Govaerts

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It is known that every ovoid of the parabolic quadric Q(4, q), q = p h , p prime, intersects every three-dimensional elliptic quadric in 1 mod p points. We present a new approach which gives us a second proof of this result and, in the case when p = 2, allows us to prove that every ovoid of Q(4, q) either intersects all the three-dimensional ellip-tic(More)
Cameron–Liebler line classes are sets of lines in PGð3; qÞ that contain a fixed number x of lines of every spread. Cameron and Liebler classified them for x A f0; 1; 2; q 2 À 1; q 2 ; q 2 þ 1g and conjectured that no others exist. This conjecture was disproven by Drudge and his counterexample was generalised to a counterexample for any odd q by Bruen and(More)
Minihypers are substructures of projective spaces introduced to study linear codes meeting the Griesmer bound. Recently, many results in finite geometry were obtained by applying characterization results on minihypers [8, 17, 18]. In this paper , using characterization results on certain minihypers, we present new results on tight sets in classical finite(More)
Introducing a connection to minihypers, we prove extendability results for partial hemisys-tems. 1 Definitions Let PG(n, q) denote the n-dimensional projective space over GF(q), the finite field of order q. If P is a point of PG(n, q), then star(P) denotes the set of lines of PG(n, q) through P. Let Q(4, q) denote the nonsingular quadric in PG(4, q) and W 3(More)
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