Quantum codes and locally recoverable codes from evaluation codes

Doctorat internacional

Detalles Bibliográficos
Autor: Martín-Cruz, Helena
Tipo de recurso: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:CBUC, CESCA
Repositorio:TDR. Tesis Doctorales en Red
OAI Identifier:oai:www.tdx.cat:10803/691958
Acceso en línea:http://hdl.handle.net/10803/691958
http://dx.doi.org/10.6035/14104.2024.838875
Access Level:acceso abierto
Palabra clave:Locally recoverable codes
Quantum codes
Evaluation codes
Error-correction
Subfield-subcodes
Monomial-Cartesian codes
Ciències
51
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spelling Quantum codes and locally recoverable codes from evaluation codesMartín-Cruz, HelenaLocally recoverable codesQuantum codesEvaluation codesError-correctionSubfield-subcodesMonomial-Cartesian codesCiències51Doctorat internacionalThis PhD thesis addresses two current problems belonging to the fields of classical and quantum information theory. The first is the repair problem in distributed and cloud storage systems in the setting where multiple nodes may fail simultaneously. These codes are called (r,\delta)-locally recoverable codes. To handle it, we consider monomial-Cartesian codes, resulting in new (r,\delta)-locally recoverable codes. The other problem is the construction of good quantum error-correcting codes. Those we provide are quantum stabilizer codes derived from two families of classical codes: generalized (or twisted) monomial-Cartesian codes and evaluation codes at the roots of trace-depending polynomials. Both quantum code constructions have excellent parameters.Programa de Doctorat en CiènciesUniversitat Jaume IHernando, FernandoGalindo, CarlosGalindo, CarlosUniversitat Jaume I. Escola de Doctorat202420242024info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersion198 p.application/pdfhttp://hdl.handle.net/10803/691958http://dx.doi.org/10.6035/14104.2024.838875TDX (Tesis Doctorals en Xarxa)reponame:TDR. Tesis Doctorales en Redinstname:CBUC, CESCAInglésL'accés als continguts d'aquesta tesi queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-sa/4.0/http://creativecommons.org/licenses/by-sa/4.0/info:eu-repo/semantics/openAccessoai:www.tdx.cat:10803/6919582026-06-14T12:46:07Z
dc.title.none.fl_str_mv Quantum codes and locally recoverable codes from evaluation codes
title Quantum codes and locally recoverable codes from evaluation codes
spellingShingle Quantum codes and locally recoverable codes from evaluation codes
Martín-Cruz, Helena
Locally recoverable codes
Quantum codes
Evaluation codes
Error-correction
Subfield-subcodes
Monomial-Cartesian codes
Ciències
51
title_short Quantum codes and locally recoverable codes from evaluation codes
title_full Quantum codes and locally recoverable codes from evaluation codes
title_fullStr Quantum codes and locally recoverable codes from evaluation codes
title_full_unstemmed Quantum codes and locally recoverable codes from evaluation codes
title_sort Quantum codes and locally recoverable codes from evaluation codes
dc.creator.none.fl_str_mv Martín-Cruz, Helena
author Martín-Cruz, Helena
author_facet Martín-Cruz, Helena
author_role author
dc.contributor.none.fl_str_mv Hernando, Fernando
Galindo, Carlos
Galindo, Carlos
Universitat Jaume I. Escola de Doctorat
dc.subject.none.fl_str_mv Locally recoverable codes
Quantum codes
Evaluation codes
Error-correction
Subfield-subcodes
Monomial-Cartesian codes
Ciències
51
topic Locally recoverable codes
Quantum codes
Evaluation codes
Error-correction
Subfield-subcodes
Monomial-Cartesian codes
Ciències
51
description Doctorat internacional
publishDate 2024
dc.date.none.fl_str_mv 2024
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/doctoralThesis
info:eu-repo/semantics/publishedVersion
format doctoralThesis
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10803/691958
http://dx.doi.org/10.6035/14104.2024.838875
url http://hdl.handle.net/10803/691958
http://dx.doi.org/10.6035/14104.2024.838875
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by-sa/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-sa/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 198 p.
application/pdf
dc.publisher.none.fl_str_mv Universitat Jaume I
publisher.none.fl_str_mv Universitat Jaume I
dc.source.none.fl_str_mv TDX (Tesis Doctorals en Xarxa)
reponame:TDR. Tesis Doctorales en Red
instname:CBUC, CESCA
instname_str CBUC, CESCA
reponame_str TDR. Tesis Doctorales en Red
collection TDR. Tesis Doctorales en Red
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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