Extremal problems on sum-free sets and coverings in tridimensional spaces
type: Item
instance of: scholarly article
title: Extremal problems on sum-free sets and coverings in tridimensional spaces
zbMATH Open document ID: 1247.94071
author: Candido F. X. de Mendonça Neto
author: Emerson L. Monte Carmelo
published in: Aequationes Mathematicae
publication date: 2011-02-02T00:00:00Z
review text: Let \(q\) be a prime power, and let \(\mathbb F_q\) be the field of order \(q\). Define \(c(q)\) to be the minimum cardinality of a subset \(H\) of \(\mathbb F_q\) such that every vector in this space differs in at most 1 coordinate from a multiple of a vector in \(H\). The authors prove that \(c(5)=4.\) Then they use a construction of short coverings from sum-free sets to prove the following. If \(q\) is odd, then \(c(q) \leq 6 \lceil {{q-1}\over{12}} \rceil + 6 \lceil \log_4({{q-1}\over{4}})\rceil +3\) and if \(q\) is even, then \(c(q) \leq 6 \lceil {{q-1}\over{9}} \rceil + 6 \lceil \log_4({{q-1}\over{3}})\rceil +3\).
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 94B75
Mathematics Subject Classification ID: 11H71
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 5843969
zbMATH Keywords: sum-free sets
zbMATH Keywords: coverings
MaRDI profile type: Publication
full work available at URL: s00010-009-2971-0
OpenAlex ID: W2061628830
DOI: 10.1007/S00010-009-2971-0
description: scientific article; zbMATH DE number 5843969