Algebraic geometric codes from elliptic curves
"Let C=[n,k,d] be a Goppa Code constructed from an elliptic curve. It is known that C is an AMDS (almost MDS) code i.e. d=n-k. By studying how many information sets C has (an MDS Code has \binom{n}{k} information sets) we investigate, for a given rate \frac{k}{n}, how close are actually Goppa C...
- Autores:
-
Jaramillo Martínez, David
- Tipo de recurso:
- Fecha de publicación:
- 2019
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/44336
- Acceso en línea:
- http://hdl.handle.net/1992/44336
- Palabra clave:
- Geometría algebraica - Investigaciones
Códigos Goppa - Investigaciones
Curvas algebráicas - Investigaciones
Matemáticas
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/4.0/
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Al consultar y hacer uso de este recurso, está aceptando las condiciones de uso establecidas por los autores.http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Karpuk, David Antonc5f52f4c-7cf9-4ee9-ac8e-fd226ba6aee0500Jaramillo Martínez, David5f25729c-7883-485a-861b-620dc80d28ed500Velasco Gregory, Mauricio FernandoGreferath, Marcus2020-09-03T14:37:34Z2020-09-03T14:37:34Z2019http://hdl.handle.net/1992/44336u827175.pdfinstname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/"Let C=[n,k,d] be a Goppa Code constructed from an elliptic curve. It is known that C is an AMDS (almost MDS) code i.e. d=n-k. By studying how many information sets C has (an MDS Code has \binom{n}{k} information sets) we investigate, for a given rate \frac{k}{n}, how close are actually Goppa Codes from being MDS, having in mind the benefit that they do not require such a big underlying field as say Reed-Solomon Codes. For the case k=3 we say exactly how far are them of being MDS."--Tomado del Formato de Documento de Grado."Sea C=[n,k,d] un código de Goppa construido a partir de una curva elíptica. Es conocido que C es un código AMDS (almost MDS) i.e. d=n-k. Al estudiar cuantos conjuntos de información tiene C (un código MDS tiene \binom{n}{k} conjuntos de información) investigamos, para un ratio fijo \frac{k}{n}, realmente qué tan cerca están los códigos de Goppa de ser MDS. Para el caso k=3 contamos exactamente la cantidad de tales conjuntos."--Tomado del Formato de Documento de Grado.Magíster en MatemáticasMaestría65 hojasapplication/pdfengUniandesMaestría en MatemáticasFacultad de CienciasDepartamento de Matemáticasinstname:Universidad de los Andesreponame:Repositorio Institucional SénecaAlgebraic geometric codes from elliptic curvesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesishttp://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/TMGeometría algebraica - InvestigacionesCódigos Goppa - InvestigacionesCurvas algebráicas - InvestigacionesMatemáticasPublicationTHUMBNAILu827175.pdf.jpgu827175.pdf.jpgIM Thumbnailimage/jpeg6102https://repositorio.uniandes.edu.co/bitstreams/535bbe25-1791-44e4-9251-fc820ab9bfe5/download990e4eb68d6fbd87347e6a14fac7c76cMD55TEXTu827175.pdf.txtu827175.pdf.txtExtracted texttext/plain99313https://repositorio.uniandes.edu.co/bitstreams/451a0630-75e7-49f3-801c-f4f29c6fe7e5/download1713f80689c587755030fad8843cfd1cMD54ORIGINALu827175.pdfapplication/pdf693724https://repositorio.uniandes.edu.co/bitstreams/6ff9c59f-d69e-4ec7-bcfc-8a67a5144d68/downloadc3f6659724539cf7ff40544fe62dd1c8MD511992/44336oai:repositorio.uniandes.edu.co:1992/443362023-10-10 19:59:40.207http://creativecommons.org/licenses/by-nc-sa/4.0/open.accesshttps://repositorio.uniandes.edu.coRepositorio institucional Sénecaadminrepositorio@uniandes.edu.co |
dc.title.es_CO.fl_str_mv |
Algebraic geometric codes from elliptic curves |
title |
Algebraic geometric codes from elliptic curves |
spellingShingle |
Algebraic geometric codes from elliptic curves Geometría algebraica - Investigaciones Códigos Goppa - Investigaciones Curvas algebráicas - Investigaciones Matemáticas |
title_short |
Algebraic geometric codes from elliptic curves |
title_full |
Algebraic geometric codes from elliptic curves |
title_fullStr |
Algebraic geometric codes from elliptic curves |
title_full_unstemmed |
Algebraic geometric codes from elliptic curves |
title_sort |
Algebraic geometric codes from elliptic curves |
dc.creator.fl_str_mv |
Jaramillo Martínez, David |
dc.contributor.advisor.none.fl_str_mv |
Karpuk, David Anton |
dc.contributor.author.none.fl_str_mv |
Jaramillo Martínez, David |
dc.contributor.jury.none.fl_str_mv |
Velasco Gregory, Mauricio Fernando Greferath, Marcus |
dc.subject.armarc.es_CO.fl_str_mv |
Geometría algebraica - Investigaciones Códigos Goppa - Investigaciones Curvas algebráicas - Investigaciones |
topic |
Geometría algebraica - Investigaciones Códigos Goppa - Investigaciones Curvas algebráicas - Investigaciones Matemáticas |
dc.subject.themes.none.fl_str_mv |
Matemáticas |
description |
"Let C=[n,k,d] be a Goppa Code constructed from an elliptic curve. It is known that C is an AMDS (almost MDS) code i.e. d=n-k. By studying how many information sets C has (an MDS Code has \binom{n}{k} information sets) we investigate, for a given rate \frac{k}{n}, how close are actually Goppa Codes from being MDS, having in mind the benefit that they do not require such a big underlying field as say Reed-Solomon Codes. For the case k=3 we say exactly how far are them of being MDS."--Tomado del Formato de Documento de Grado. |
publishDate |
2019 |
dc.date.issued.es_CO.fl_str_mv |
2019 |
dc.date.accessioned.none.fl_str_mv |
2020-09-03T14:37:34Z |
dc.date.available.none.fl_str_mv |
2020-09-03T14:37:34Z |
dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/masterThesis |
dc.type.content.spa.fl_str_mv |
Text |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TM |
dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/1992/44336 |
dc.identifier.pdf.none.fl_str_mv |
u827175.pdf |
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reponame:Repositorio Institucional Séneca |
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repourl:https://repositorio.uniandes.edu.co/ |
url |
http://hdl.handle.net/1992/44336 |
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u827175.pdf instname:Universidad de los Andes reponame:Repositorio Institucional Séneca repourl:https://repositorio.uniandes.edu.co/ |
dc.language.iso.es_CO.fl_str_mv |
eng |
language |
eng |
dc.rights.uri.*.fl_str_mv |
http://creativecommons.org/licenses/by-nc-sa/4.0/ |
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info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ http://purl.org/coar/access_right/c_abf2 |
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openAccess |
dc.format.extent.es_CO.fl_str_mv |
65 hojas |
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application/pdf |
dc.publisher.es_CO.fl_str_mv |
Uniandes |
dc.publisher.program.es_CO.fl_str_mv |
Maestría en Matemáticas |
dc.publisher.faculty.es_CO.fl_str_mv |
Facultad de Ciencias |
dc.publisher.department.es_CO.fl_str_mv |
Departamento de Matemáticas |
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