On the cylinder conjecture

Sam Mattheus; Jan De Beule; Jeroen Demeyer; Peter Sziklai

doi:10.1007/s10623-018-0571-5

On the cylinder conjecture

Sam Mattheus, Jan De Beule, Jeroen Demeyer, Peter Sziklai

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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≤ 13. This result also slightly refines a result of Sziklai on point sets in AG (3 , p).

Original language	English
Pages (from-to)	879-893
Number of pages	15
Journal	Designs, Codes and Cryptography
Volume	87
Issue number	4
DOIs	https://doi.org/10.1007/s10623-018-0571-5
Publication status	Published - 15 Apr 2019

Keywords

Affine space
Cylinder conjecture
Polynomial method

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AU - De Beule, Jan

AU - Demeyer, Jeroen

AU - Sziklai, Peter

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AB - 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≤ 13. This result also slightly refines a result of Sziklai on point sets in AG (3 , p).

KW - Affine space

KW - Cylinder conjecture

KW - Polynomial method

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JF - Designs, Codes and Cryptography

SN - 0925-1022

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On the cylinder conjecture

Abstract

Keywords

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