Showing papers by "Joseph A. Thas published in 1992"
TL;DR: In this article, the existence and non-existence theorems on spreads and ovoids of finite classical polar spaces are surveyed and upper bounds for their sizes are obtained, including partial spreads and partial ovoids.
Abstract: This paper surveys the existence and non-existence theorems on spreads and ovoids of finite classical polar spaces Several of the results are new Further, partial spreads and partial ovoids of finite polar spaces are introduced and upper bounds for their sizes are obtained
59 citations
29 citations
01 Jan 1992
TL;DR: A survey of important results on k-arcs can be found in this paper, in particular the answers to three fundamental problems on arcs posed by B. Segre in 1955.
Abstract: Let C be a code of length k over an alphabet A of size q greather or equal 2 . Having chosen m with 2 m k we impose the following condition on C : no two words agree in as many as m positions. It then follows that |C| q m . If |C|=q m , then C is called a Maximum Distance Separable code (M.D.S. code). A k -arc in PG(n,q) is a set K of k points with k at least n+1 such that no n+1 points lie in a hyperplane. It can be shown that arcs and linear M.D.S. codes are equivalent objects. Here we give a survey of important results on k -arcs, in particular we survey the answers to three fundamental problems on arcs posed by B. Segre in 1955.
23 citations
TL;DR: In this article, it was shown that for any prime power q, the absolute points and nonabsolute lines of a unitary polarity of PG(2, q2) form a unital that is called the classical unital.
Abstract: A unital U with parameter q is a 2 − (q3 + 1, q + 1, 1) design. If a point set U in PG(2, q2) together with its (q + 1)-secants forms a unital, then U is called a Hermitian arc. Through each point p of a Hermitian arc H there is exactly one line L having with H only the point p in commons this line L is called the tangent of H at p. For any prime power q, the absolute points and nonabsolute lines of a unitary polarity of PG(2, q2) form a unital that is called the classical unital. The points of a classical unital are the points of a Hermitian curve in PG(2, q2).
Let H be a Hermitian arc in the projective plane PG(2, q2). If tangents of H at collinear points of H are concurrent, then H is a Hermitian curve. This result proves a well known conjecture on Hermitian arcs.
22 citations
TL;DR: The theorems show that the classification of all complete k -arcs in PG( n, q ), q even and q − 2 ⩾ n > q − q 2 − 11 4, is closely related to the Classification of all ( q +2)-arcsin PG(2, q ).
15 citations
TL;DR: An extension of Segre's generalization of Menelaus' theorem to an arbitrary collection of lines is given in this article, where an extension is given to the problem of enumerating a set of lines.
Abstract: An extension is given of Segre's generalization of Menelaus' theorem to an arbitrary collection of lines.
7 citations