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We present results on the size of the smallest maximal partial ovoids and on the size of the smallest maximal partial spreads of the generalized quadrangles W (q) and Q(4, q).
In 1969, Denniston gave a construction of maximal arcs of degree d in Desarguesian projective planes of even order q, for all d dividing q. In 2002 Mathon gave a construction method generalizing the one of Denniston. We will give a new geometric approach to these maximal arcs. This will allow us to count the number of non-isomorphic Mathon maximal arcs of… (More)
Let Π = (P, L, I) denote a rank two geometry. In this paper, we are interested in the largest value of |X||Y | where X ⊂ P and Y ⊂ L are sets such that (X ×Y)∩I = ∅. Let α(Π) denote this value. We concentrate on the case where P is the point set of PG(n, q) and L is the set of k-spaces in PG(n, q). In the case that Π is the projective plane PG(2, q),… (More)
In this note we characterize thick finite generalized quadrangles constructed from a generalized hyperoval as those admitting an abelian Singer group, i.e., an abelian group acting regularly on the points.
In this article, we prove that amongst all n by n bipartite graphs of girth at least six, where n = q 2 + q + 1 ≥ 157, the incidence graph of a projective plane of order q, when it exists, has the maximum number of cycles of length eight. This characterizes projective planes as the partial planes with the maximum number of quadrilaterals.
3 Multi-step majority logic decoding and the modified finite geometry designs. 39
In  De Clerck, De Winter and Maes counted the number of non-isomorphic Mathon maximal arcs of degree 8 in PG(2, 2 h), h = 7 and prime. In this article we will show that in PG(2, 2 7) a special class of Mathon maximal arcs of degree 8 arises which admits a Singer group (i.e. a sharply transitive group) on the 7 conics of these arcs. We will give a… (More)