Two characterizations of the family of secant lines of an ovoid of PG(3, $${\varvec{q}}$$ q )
TL;DR: In this paper, two characterizations of the family of secant lines to an ovoid of polygonal O(3, q) are given, where q is the length of the secant line.
Abstract: Two new characterizations of the family of secant lines to an ovoid of $$\mathrm {PG}(3, q)$$
are given.
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TL;DR: A particular Pappus configuration gives us the road map for an excursion into the world of small finite geometries as mentioned in this paper, which is the basis for our work here.
Abstract: A particular Pappus configuration gives us the road map for an excursion into the world of small finite geometries.
2 citations
Cites result from "Two characterizations of the family..."
...The study of finite configurations is a broad area which has a unity not merely of description but also in practice, since many of the figures studied give results which can be applied to other, apparently dissimilar structures, see [4], [9], [10], [16] and [17]....
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TL;DR: In this paper, the set of external points of a conic in PG, (2, q) odd, within the odd set of points of the conic is characterized.
Abstract: Recently, see [1], Alabdullah and Hirschfeld introduce the type of a point. This simple and original concept allow us to characterize the set of external points of a conic in PG, (2, q) odd, within...
1 citations
Cites background from "Two characterizations of the family..."
...Since incidence is one of the earliest properties known to both mankind and mathematicians, a natural and important combinatorial problem is to classify sets with given intersection numbers, see, for istance, [1], [8], [9], [10], [15], [17], [21], [22], [23], [24], and [25]....
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Book•
20 Feb 1986
TL;DR: Projective Geometrics Over Finite Fields (OUP, 1979) as mentioned in this paper considers projective spaces of three dimensions over a finite field and examines properties of four and five dimensions, fundamental applications to translation planes, simple groups, and coding theory.
Abstract: This self-contained and highly detailed study considers projective spaces of three dimensions over a finite field It is the second and core volume of a three-volume treatise on finite projective spaces, the first volume being Projective Geometrics Over Finite Fields (OUP, 1979) The present work restricts itself to three dimensions, and considers both topics which are analogous of geometry over the complex numbers and topics that arise out of the modern theory of incidence structures The book also examines properties of four and five dimensions, fundamental applications to translation planes, simple groups, and coding theory
713 citations
35 citations
TL;DR: In this paper, the authors characterized the family of secant lines of an ovoid of PG$(3,q)$ and the external lines of a polygonal ovoid.
Abstract: In this paper we characterize the family of secant lines of an ovoid of PG$(3,q)$ and the family of external lines to an ovoid of PG$(3,q)$.
13 citations
TL;DR: A new proof is given of the characterization of the external lines of a hyperoval cone in PG(3,q), q even by giving a new proof without using that particular hypothesis.
10 citations