Journal ArticleDOI
Arcs in projective planes over prime fields
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This article is published in Journal of Geometry.The article was published on 1990-07-01. It has received 49 citations till now. The article focuses on the topics: Projective plane & Projective space.read more
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Book ChapterDOI
The packing problem in statistics, coding theory and finite projective spaces : update 2001
J. W. P. Hirschfeld,Leo Storme +1 more
TL;DR: In this paper, the authors updated the 1998 survey on the packing problem, up to 1995, and showed that considerable progress has been made on different kinds of subconfigurations over the last few decades.
Journal ArticleDOI
The packing problem in statistics, coding theory and finite projective spaces
J. W. P. Hirschfeld,Leo Storme +1 more
TL;DR: In this paper, the authors considered the problem of finding the largest size of a point set in a set of points in a projective space and showed that it is equivalent to the packing problem in geometry.
Book ChapterDOI
Projective Geometry over a Finite Field
TL;DR: In this article, the authors focus on projective geometry over a finite field and define a k-arc in projective plane, PG (n, q) is a set K of k points with k ≥ n + 1 such that no n+ 1 points of K lie in a hyperplane.
Journal ArticleDOI
On sets of vectors of a finite vector space in which every subset of basis size is a basis II
Simeon Ball,Jan De Beule +1 more
TL;DR: This article contains a proof of the MDS conjecture for k ≤ 2p − 2, that if S is a set of vectors of Q in which every subset of S of size k is a basis, then |S| ≤ q + 1.
Book
Finite Geometry and Combinatorial Applications
TL;DR: In this article, the forbidden subgraph problem is formulated as a MDS code problem and solutions to the exercises are given. Appendix A Solution to the problem Appendix B Additional proofs Appendix C Notes and references References Index
References
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Book
Projective geometries over finite fields
TL;DR: The first properties of the plane can be found in this article, where the authors define the following properties: 1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. Ovals 9. Arithmetic of arcs of degree two 10. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes 15.
Journal ArticleDOI
Weierstrass Points and Curves Over Finite Fields
TL;DR: Stohr et al. as discussed by the authors showed that the Riemann hypothesis for algebraic curves over finite fields can be improved by using the Weierstrass order-sequence associated with the projective embedding.
Book ChapterDOI
Caps in Elliptic Quadrics
TL;DR: In this paper, the authors discuss the caps in elliptic quadrics and show that the three conics of a tetrahedral system are contained in a quadric if and only if the system is flat: the quadric is then unique and irreducible.