Journal ArticleDOI
A characterization of hermitian curves
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This article is published in Journal of Geometry.The article was published on 1991-04-01. It has received 31 citations till now. The article focuses on the topics: Hermitian matrix.read more
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Journal Article
A characterization of Hermitian function fields over finite fields.
TL;DR: A function field is called maximal if N is equal to the upper bound r + l + 2gyr as mentioned in this paper, and a necessary condition for maximality is that r is a square.
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
The genus of curves over finite fields with many rational points
Rainer Fuhrmann,Fernando Torres +1 more
TL;DR: In this paper, it was shown that the genus of a projective, irreducible non-singular algebraic curve over the finite field with a number of rational points attains the Hasse-Weil bound.
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On weierstrass points and optimal curves
Rainer Fuhrmann,Fernando Torres +1 more
TL;DR: In this article, the authors show some properties of maximal curves and give a characterization of the Suzuki curve by means of its genus and the number of its rational points only, which is a characterization based on the number and genus of the rational points.
Journal ArticleDOI
Open problems in finite projective spaces
TL;DR: Most of the objects studied in this paper have an interesting group; the classical groups and other finite simple groups appear in this way.
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.
Book
Finite projective spaces of three dimensions
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.
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
Complete Arcs in Planes of Square Order
TL;DR: In the Desarguesian plane of even square order, the upper bound for complete arcs other than ovals was shown in this article, where large arcs in cyclic planes of square order are constructed as orbits of a subgroup of a group whose generator acts as a single cycle.