{"id":18469,"date":"2018-03-09T09:07:00","date_gmt":"2018-03-09T09:07:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/pesos-de-hamming-generalizados-en-codigos-algebro-geometricos\/"},"modified":"2018-03-09T09:07:00","modified_gmt":"2018-03-09T09:07:00","slug":"pesos-de-hamming-generalizados-en-codigos-algebro-geometricos","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/pesos-de-hamming-generalizados-en-codigos-algebro-geometricos\/","title":{"rendered":"Pesos de hamming generalizados en c\u00f3digos \u00e1lgebro-geom\u00e9tricos"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Domingo Ram\u00edrez Alzola <\/strong><\/h2>\n<p>Motivados por sus aplicaciones criptogr\u00e1ficas, no planteamos en esta memoria el estudio de los pesos de hamming generalizados para c\u00f3digos \u00e1lgebro-geom\u00e9tricos.  hemos partido de una curva arbitraria y a partir de ella hemos constru\u00eddo un c\u00f3digo \u00e1lgebro-geom\u00e9trico. Utilizando las propiedades de la curva y la cota del orden, hemos calculado y\/o estimado ciertos pesos de hamming para dichos c\u00f3digos.  teniendo en cuenta que nuestro planteamiento del problema ha sido general, lo hemos aplicado a un tipo particular de c\u00f3digos que son los c\u00f3digos hermitianos. los resultados anteriores junto con ciertas propiedades adicionales de la curva hermitiana nos ha permitido calcular la segunda y tercera distancias para dichos c\u00f3digos.  visto que la cota del orden ha dado un buen resultado, lo hemos intentado aplicar a otro de tipo de c\u00f3digos, englobados dentro de los c\u00f3digos \u00e1lgebro-geom\u00e9tricos, que son los c\u00f3digos hiperel\u00edpticos. En este caso, hemos logrado dar los pesos cuando \u00abm\u00bb es mayor o igual que \u00abn\u00bb pero no nos ha servido en el otro caso. En dicho caso, y bas\u00e1ndonos en una idea de m. De boer, hemos conseguido dar la jerarqu\u00eda completa salvo en un caso. A continuaci\u00f3n, hemos dado un m\u00e9todo de construcci\u00f3n de curvas hiperel\u00edpticas para las cuales hemos determinado la jerarqu\u00eda por completo.  para finalizar con la memoria, hemos enfocado el problema desde otro punto de vista. En concreto, se trata de estimar los pesos de hamming generalizados v\u00eda cardinales de conjuntos de ceros comunes a ciertos polinomios. El resultado ha sido que hemos logrado acotar la jerarqu\u00eda para un tipo particular de c\u00f3digos hermitianos. Las cotas superiores obtenidas se han convertido en igualdad en un caso particular con la ayuda de la cota \u00abfootprint\u00bb.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Pesos de hamming generalizados en c\u00f3digos \u00e1lgebro-geom\u00e9tricos<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Pesos de hamming generalizados en c\u00f3digos \u00e1lgebro-geom\u00e9tricos <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Domingo Ram\u00edrez Alzola <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Pa\u00eds vasco\/euskal herriko unibertsitatea<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 15\/07\/2002<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Juan  Gabriel Tena Ayuso<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: lloren\u00ed\u00a7 Huguet rotger <\/li>\n<li>josep Rifa coma (vocal)<\/li>\n<li>santos Gonz\u00e1lez jim\u00e9nez (vocal)<\/li>\n<li>fausto Montoya vitini (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Domingo Ram\u00edrez Alzola Motivados por sus aplicaciones criptogr\u00e1ficas, no planteamos en esta memoria el estudio de los [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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