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Designs, Codes and Cryptography

Erschienen in:

13.10.2018

On the cylinder conjecture

verfasst von: Jan De Beule, Jeroen Demeyer, Sam Mattheus, Péter Sziklai

Erschienen in: Designs, Codes and Cryptography | Ausgabe 4/2019

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Abstract

In this paper, we associate a weight function with a set of points satisfying the conditions of the cylinder conjecture. Then we derive properties of this weight function using the Rédei polynomial of the point set. Using additional assumptions on the number of non-determined directions, together with an exhaustive computer search for weight functions satisfying particular properties, we prove a relaxed version of the cylinder conjecture for \(p \le 13\). This result also slightly refines a result of Sziklai on point sets in \(\mathrm {AG}(3,p)\).

Vorheriger Artikel Relative blocking sets of unions of Baer subplanes

Nächster Artikel A variation of the dual hyperoval using presemifields

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Blokhuis A., Marino G., Mazzocca F.: Generalized hyperfocused arcs in \(PG(2, p)\). J. Comb. Des. 22(12), 506–513 (2014).MathSciNetCrossRefMATH

Sziklai P.: Directions in \({\rm AG}(3, p)\) and their applications. Note Mat. 26(1), 121–130 (2006).MathSciNetMATH

Titel: On the cylinder conjecture
verfasst von: Jan De Beule
Jeroen Demeyer
Sam Mattheus
Péter Sziklai
Publikationsdatum: 13.10.2018
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 4/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0571-5

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