On additive MDS codes with linear projections

We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let C be an -linear MDS code over . If , , , and C has three coordinates from which its projections are equivalent to -linear codes, we prove that C itself is equivalent to...

Full description

Bibliographic Details
Authors: Adriaensen, Sam, Ball, Simeon Michael|||0000-0003-4845-2084
Format: article
Publication Date:2023
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/404608
Online Access:https://hdl.handle.net/2117/404608
https://dx.doi.org/10.1016/j.ffa.2023.102255
Access Level:Open access
Keyword:Geometry
Error-correcting codes (Information theory)
Geometria finita
Codis de correcció d'errors (Teoria de la informació)
Classificació AMS::51 Geometry::51E Finite geometry and special incidence structures
Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
Àrees temàtiques de la UPC::Matemàtiques i estadística
id ES_9c12cd83ef50e37747c2ad61a42eceb2
oai_identifier_str oai:upcommons.upc.edu:2117/404608
network_acronym_str ES
network_name_str España
repository_id_str
spelling On additive MDS codes with linear projectionsAdriaensen, SamBall, Simeon Michael|||0000-0003-4845-2084GeometryError-correcting codes (Information theory)Geometria finitaCodis de correcció d'errors (Teoria de la informació)Classificació AMS::51 Geometry::51E Finite geometry and special incidence structuresClassificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codesÀrees temàtiques de la UPC::Matemàtiques i estadística::GeometriaÀrees temàtiques de la UPC::Matemàtiques i estadísticaWe support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let C be an -linear MDS code over . If , , , and C has three coordinates from which its projections are equivalent to -linear codes, we prove that C itself is equivalent to an -linear code. If , , and there are two disjoint subsets of coordinates whose combined size is at most from which the projections of C are equivalent to -linear codes, we prove that C is equivalent to a code which is linear over a larger field than .Peer ReviewedElsevier20232023-10-0120242024-03-14journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/404608https://dx.doi.org/10.1016/j.ffa.2023.102255reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113082GB-I00 COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4046082026-05-27T15:37:01Z
dc.title.none.fl_str_mv On additive MDS codes with linear projections
title On additive MDS codes with linear projections
spellingShingle On additive MDS codes with linear projections
Adriaensen, Sam
Geometry
Error-correcting codes (Information theory)
Geometria finita
Codis de correcció d'errors (Teoria de la informació)
Classificació AMS::51 Geometry::51E Finite geometry and special incidence structures
Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short On additive MDS codes with linear projections
title_full On additive MDS codes with linear projections
title_fullStr On additive MDS codes with linear projections
title_full_unstemmed On additive MDS codes with linear projections
title_sort On additive MDS codes with linear projections
dc.creator.none.fl_str_mv Adriaensen, Sam
Ball, Simeon Michael|||0000-0003-4845-2084
author Adriaensen, Sam
author_facet Adriaensen, Sam
Ball, Simeon Michael|||0000-0003-4845-2084
author_role author
author2 Ball, Simeon Michael|||0000-0003-4845-2084
author2_role author
dc.subject.none.fl_str_mv Geometry
Error-correcting codes (Information theory)
Geometria finita
Codis de correcció d'errors (Teoria de la informació)
Classificació AMS::51 Geometry::51E Finite geometry and special incidence structures
Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Geometry
Error-correcting codes (Information theory)
Geometria finita
Codis de correcció d'errors (Teoria de la informació)
Classificació AMS::51 Geometry::51E Finite geometry and special incidence structures
Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
Àrees temàtiques de la UPC::Matemàtiques i estadística
description We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let C be an -linear MDS code over . If , , , and C has three coordinates from which its projections are equivalent to -linear codes, we prove that C itself is equivalent to an -linear code. If , , and there are two disjoint subsets of coordinates whose combined size is at most from which the projections of C are equivalent to -linear codes, we prove that C is equivalent to a code which is linear over a larger field than .
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-10-01
2024
2024-03-14
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/2117/404608
https://dx.doi.org/10.1016/j.ffa.2023.102255
url https://hdl.handle.net/2117/404608
https://dx.doi.org/10.1016/j.ffa.2023.102255
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113082GB-I00 COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869414626010071040
score 15,300724

Similar Items