Dual toric codes and polytopes of degree one

We define a statistical measure of the typical size of words of low weight in a linear code over a finite field. We prove that the dual toric codes coming from polytopes of degree one are characterized, among all dual toric codes, by being extremal with respect to this measure. We also give a geomet...

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Autores:
Tipo de recurso:
Fecha de publicación:
2015
Institución:
Universidad del Rosario
Repositorio:
Repositorio EdocUR - U. Rosario
Idioma:
eng
OAI Identifier:
oai:repository.urosario.edu.co:10336/23299
Acceso en línea:
https://doi.org/10.1137/140966228
https://repository.urosario.edu.co/handle/10336/23299
Palabra clave:
Topology
Exact formulas
Finite fields
Geometric interpretation
Linear codes
Minimal degree
Minimum distance
Statistical measures
Toric varieties
Codes (symbols)
Codes over finite fields
Toric varieties
Varieties of minimal degree
Rights
License
Abierto (Texto Completo)
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network_acronym_str EDOCUR2
network_name_str Repositorio EdocUR - U. Rosario
repository_id_str
spelling 09b3ee6b-73cc-4abc-b77c-b0de6472438f-12843d604-b6c5-43cc-868e-77af551542f9-12020-05-26T00:01:00Z2020-05-26T00:01:00Z2015We define a statistical measure of the typical size of words of low weight in a linear code over a finite field. We prove that the dual toric codes coming from polytopes of degree one are characterized, among all dual toric codes, by being extremal with respect to this measure. We also give a geometric interpretation of the minimum distance of dual toric codes and characterize its extremal values. Finally, we obtain exact formulas for the parameters of both primal and dual toric codes associated to polytopes of degree one. © 2015 Society for Industrial and Applied Mathematics.application/pdfhttps://doi.org/10.1137/1409662281095714608954801https://repository.urosario.edu.co/handle/10336/23299engSociety for Industrial and Applied Mathematics Publications692No. 1683SIAM Journal on Discrete MathematicsVol. 29SIAM Journal on Discrete Mathematics, ISSN:10957146, 08954801, Vol.29, No.1 (2015); pp. 683-692https://www.scopus.com/inward/record.uri?eid=2-s2.0-84982296411&doi=10.1137%2f140966228&partnerID=40&md5=f6db4e6d2f9eef4ce95e6a1c5f5d2238Abierto (Texto Completo)http://purl.org/coar/access_right/c_abf2instname:Universidad del Rosarioreponame:Repositorio Institucional EdocURTopologyExact formulasFinite fieldsGeometric interpretationLinear codesMinimal degreeMinimum distanceStatistical measuresToric varietiesCodes (symbols)Codes over finite fieldsToric varietiesVarieties of minimal degreeDual toric codes and polytopes of degree onearticleArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501Umaña V.G.Velasco M.10336/23299oai:repository.urosario.edu.co:10336/232992022-05-02 07:37:20.916171https://repository.urosario.edu.coRepositorio institucional EdocURedocur@urosario.edu.co
dc.title.spa.fl_str_mv Dual toric codes and polytopes of degree one
title Dual toric codes and polytopes of degree one
spellingShingle Dual toric codes and polytopes of degree one
Topology
Exact formulas
Finite fields
Geometric interpretation
Linear codes
Minimal degree
Minimum distance
Statistical measures
Toric varieties
Codes (symbols)
Codes over finite fields
Toric varieties
Varieties of minimal degree
title_short Dual toric codes and polytopes of degree one
title_full Dual toric codes and polytopes of degree one
title_fullStr Dual toric codes and polytopes of degree one
title_full_unstemmed Dual toric codes and polytopes of degree one
title_sort Dual toric codes and polytopes of degree one
dc.subject.keyword.spa.fl_str_mv Topology
Exact formulas
Finite fields
Geometric interpretation
Linear codes
Minimal degree
Minimum distance
Statistical measures
Toric varieties
Codes (symbols)
Codes over finite fields
Toric varieties
Varieties of minimal degree
topic Topology
Exact formulas
Finite fields
Geometric interpretation
Linear codes
Minimal degree
Minimum distance
Statistical measures
Toric varieties
Codes (symbols)
Codes over finite fields
Toric varieties
Varieties of minimal degree
description We define a statistical measure of the typical size of words of low weight in a linear code over a finite field. We prove that the dual toric codes coming from polytopes of degree one are characterized, among all dual toric codes, by being extremal with respect to this measure. We also give a geometric interpretation of the minimum distance of dual toric codes and characterize its extremal values. Finally, we obtain exact formulas for the parameters of both primal and dual toric codes associated to polytopes of degree one. © 2015 Society for Industrial and Applied Mathematics.
publishDate 2015
dc.date.created.spa.fl_str_mv 2015
dc.date.accessioned.none.fl_str_mv 2020-05-26T00:01:00Z
dc.date.available.none.fl_str_mv 2020-05-26T00:01:00Z
dc.type.eng.fl_str_mv article
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.spa.spa.fl_str_mv Artículo
dc.identifier.doi.none.fl_str_mv https://doi.org/10.1137/140966228
dc.identifier.issn.none.fl_str_mv 10957146
08954801
dc.identifier.uri.none.fl_str_mv https://repository.urosario.edu.co/handle/10336/23299
url https://doi.org/10.1137/140966228
https://repository.urosario.edu.co/handle/10336/23299
identifier_str_mv 10957146
08954801
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.citationEndPage.none.fl_str_mv 692
dc.relation.citationIssue.none.fl_str_mv No. 1
dc.relation.citationStartPage.none.fl_str_mv 683
dc.relation.citationTitle.none.fl_str_mv SIAM Journal on Discrete Mathematics
dc.relation.citationVolume.none.fl_str_mv Vol. 29
dc.relation.ispartof.spa.fl_str_mv SIAM Journal on Discrete Mathematics, ISSN:10957146, 08954801, Vol.29, No.1 (2015); pp. 683-692
dc.relation.uri.spa.fl_str_mv https://www.scopus.com/inward/record.uri?eid=2-s2.0-84982296411&doi=10.1137%2f140966228&partnerID=40&md5=f6db4e6d2f9eef4ce95e6a1c5f5d2238
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.acceso.spa.fl_str_mv Abierto (Texto Completo)
rights_invalid_str_mv Abierto (Texto Completo)
http://purl.org/coar/access_right/c_abf2
dc.format.mimetype.none.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Society for Industrial and Applied Mathematics Publications
institution Universidad del Rosario
dc.source.instname.spa.fl_str_mv instname:Universidad del Rosario
dc.source.reponame.spa.fl_str_mv reponame:Repositorio Institucional EdocUR
repository.name.fl_str_mv Repositorio institucional EdocUR
repository.mail.fl_str_mv edocur@urosario.edu.co
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