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Inclusion-maximal integral point sets over finite fields

URN to cite this document: urn:nbn:de:bvb:703-opus-4180

Title data

Kiermaier, Michael ; Kurz, Sascha:
Inclusion-maximal integral point sets over finite fields.
Bayreuth , 2007

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Abstract

We consider integral point sets in affine planes over finite fields. Here an integral point set is a set of points in $GF(q)^2$ where the formally defined Euclidean distance of every pair of points is an element of $GF(q)$. From another point of view we consider point sets over $GF(q)^2$ with few and prescribed directions. So this is related to Redeis work. Another motivation comes from the field of ordinary integral point sets in Euclidean spaces. In this article we study the spectrum of integral point sets over $GF(q)^2$ which are maximal with respect to inclusion. We give some theoretical results, constructions, conjectures, and some numerical data.

Abstract in another language

Wir betrachten ganzzahlige Punktmengen in affinen Ebenen über endlichen Körpern. Eine ganzzahlige Punktmenge ist hier eine Teilmenge von GF(q)^2, bei der der formal definierte Euklidische Abstand zwischen je zwei Punkten im Körper GF(q) liegt. In diesem Artikel betrachten wir das Spektrum der Kardinalitäten von inklusionsmaximalen ganzzahligen Punktmengen über GF(q)^2.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): msc: 51E20
Keywords: Kombinatorik; Galois-Feld; ganzzahlige Abstände; erschöpfende Suche; endliche Geometrie; Paley-Graphen; integral distances; exhaustive search; finite geometry; Paley graphs
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy > Chair Mathematics in Economy - Univ.-Prof. Dr. Jörg Rambau
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-opus-4180
Date Deposited: 25 Apr 2014 11:23
Last Modified: 27 Mar 2019 13:18
URI: https://epub.uni-bayreuth.de/id/eprint/652

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