Extending small arcs to large arcs

This is a post-peer-review, pre-copyedit version of an article published in European Journal of Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s40879-017-0193-x

Detalles Bibliográficos
Autor: Ball, Simeon Michael|||0000-0003-4845-2084
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/116509
Acceso en línea:https://hdl.handle.net/2117/116509
https://dx.doi.org/10.1007/s40879-017-0193-x
Access Level:acceso abierto
Palabra clave:Combinatorial analysis
arcs
projective spaces
MDS codes
MDS conjecture
Codificació, Teoria de la
Àrees temàtiques de la UPC::Matemàtiques i estadística
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repository_id_str
spelling Extending small arcs to large arcsBall, Simeon Michael|||0000-0003-4845-2084Combinatorial analysisarcsprojective spacesMDS codesMDS conjectureCodificació, Teoria de laÀrees temàtiques de la UPC::Matemàtiques i estadísticaThis is a post-peer-review, pre-copyedit version of an article published in European Journal of Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s40879-017-0193-xAn arc is a set of vectors of the k-dimensional vector space over the finite field with q elements Fq , in which every subset of size k is a basis of the space, i.e. every k-subset is a set of linearly independent vectors. Given an arc G in a space of odd characteristic, we prove that there is an upper bound on the largest arc containing G. The bound is not an explicit bound but is obtained by computing properties of a matrix constructed from G. In some cases we can also determine the largest arc containing G, or at least determine the hyperplanes which contain exactly k-2 vectors of the large arc. The theorems contained in this article may provide new tools in the computational classification and construction of large arcs.20182018-03-0120182018-04-20journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/116509https://dx.doi.org/10.1007/s40879-017-0193-xreponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1165092026-05-27T15:37:01Z
dc.title.none.fl_str_mv Extending small arcs to large arcs
title Extending small arcs to large arcs
spellingShingle Extending small arcs to large arcs
Ball, Simeon Michael|||0000-0003-4845-2084
Combinatorial analysis
arcs
projective spaces
MDS codes
MDS conjecture
Codificació, Teoria de la
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Extending small arcs to large arcs
title_full Extending small arcs to large arcs
title_fullStr Extending small arcs to large arcs
title_full_unstemmed Extending small arcs to large arcs
title_sort Extending small arcs to large arcs
dc.creator.none.fl_str_mv Ball, Simeon Michael|||0000-0003-4845-2084
author Ball, Simeon Michael|||0000-0003-4845-2084
author_facet Ball, Simeon Michael|||0000-0003-4845-2084
author_role author
dc.subject.none.fl_str_mv Combinatorial analysis
arcs
projective spaces
MDS codes
MDS conjecture
Codificació, Teoria de la
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Combinatorial analysis
arcs
projective spaces
MDS codes
MDS conjecture
Codificació, Teoria de la
Àrees temàtiques de la UPC::Matemàtiques i estadística
description This is a post-peer-review, pre-copyedit version of an article published in European Journal of Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s40879-017-0193-x
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-03-01
2018
2018-04-20
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/116509
https://dx.doi.org/10.1007/s40879-017-0193-x
url https://hdl.handle.net/2117/116509
https://dx.doi.org/10.1007/s40879-017-0193-x
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
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