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...

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Autores:: Jaramillo Martínez, David

Tipo de recurso:

Fecha de publicación:: 2019

Institución:: Universidad de los Andes

Repositorio:: Séneca: repositorio Uniandes

Idioma:: eng

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spelling	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
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dc.type.content.spa.fl_str_mv	Text
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dc.language.iso.es_CO.fl_str_mv	eng
language	eng
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dc.format.extent.es_CO.fl_str_mv	65 hojas
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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
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Algebraic geometric codes from elliptic curves

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