On the cylinder conjecture

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 wi...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2019-04, Vol.87 (4), p.879-893
Main Authors: De Beule, Jan, Demeyer, Jeroen, Mattheus, Sam, Sziklai, Péter
Format: Article
Language:English
Subjects:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Cylinders
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
Polynomials
Special Issue: Finite Geometries
Weighting functions
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Summary: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 ) .
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-018-0571-5