{"id":13363,"date":"2018-03-09T08:59:36","date_gmt":"2018-03-09T08:59:36","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/sobre-el-rango-y-el-nucleo-de-los-codigos-perfectos\/"},"modified":"2018-03-09T08:59:36","modified_gmt":"2018-03-09T08:59:36","slug":"sobre-el-rango-y-el-nucleo-de-los-codigos-perfectos","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/sobre-el-rango-y-el-nucleo-de-los-codigos-perfectos\/","title":{"rendered":"Sobre el rango y el nucleo de los codigos perfectos"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Merce Villanueva Gay <\/strong><\/h2>\n<p>Sea f un espacio vectorial de dimension n sobre gf(q). Un codigo q-ario c de longitud n es un codigo perfecto si para algun entero r no negativo, cada elemento de f esta a distancia menor o igual que r de exactamente una palabra codigo de c. El unico valor para el cual exiten codigos perfectos no equivalentes es r=1, los codigos q-arios 1-perfectos. Estos tienen longitud n=(q m-1)\/(q-1), q (n-m) palabras codigo y distancia minima 3.  en esta tesis, nos centramos en dos propiedades estructurales de los codigos perfectos no lineales, el rango y la dimensi\u00f3n del nucleo. El rango de un codigo c, r(c), es simplemente la dimensi\u00f3n del subespacio generado por c. El nucleo de un codigo binario es el conjunto de traslaciones que fijan en codigo. Su dimension la denotaremos por k(c). Estos dos parametros dan informacion sobre la linealidad del codigo y pueden ayudar a establecer una clasificacion.  los rangos de los codigos binarios 1-perfectos han estado investigados por etzion y vardy, quienes demostraron que existen codigos 1-perfectos para todos los rangos posibles. Phelps y levan obtuvieron codigos binarios 1-perfectos con nucleos de todas las medidas posibles. El problema principal que analizaremos en esta tesis es para que parejas de numeros (r,k) existe un codigo 1-perfecto binario c de longitud n que tenga r(c)=r y k(c)=k.  en general, estableceremos la cota superior y la inferior exactas para la dimension del nucleo de codigos binarios 1-perfectos fijado el rango, excepto para un caso. Para c\u00f3digos de rago m\u00e1ximo, r(c)=n, daremos una cota superior pero no demostraremos que es exacta. A pesar de esto, ya es conocido que a partir de m mayor o igual a 10 esta cota es exacta. Utilizaremos las construcciones doubling y switching para construir codigos 1-perfectos para todos los nucleos posibles entre estas cotas. Obtendremos un gran numero de casos pero no resolveremos completamente el problema, parcialmente porque necesitamos construir<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Sobre el rango y el nucleo de los codigos perfectos<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Sobre el rango y el nucleo de los codigos perfectos <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Merce Villanueva Gay <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Aut\u00f3noma de barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 19\/10\/2001<\/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>T. Phelps Kevin<\/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>Juan  gabriel Tena ayuso (vocal)<\/li>\n<li>j. Dejter italo (vocal)<\/li>\n<li>jaume-Luis Garcia roig (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Merce Villanueva Gay Sea f un espacio vectorial de dimension n sobre gf(q). Un codigo q-ario c [&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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[2809,1890,12500,15966,126],"tags":[29401,43412,12502,12504,43410,43411],"class_list":["post-13363","post","type-post","status-publish","format-standard","hentry","category-algebra","category-ciencia-de-los-ordenadores","category-codigo-y-sistemas-de-codificacion","category-computacion-digital","category-matematicas","tag-j-dejter-italo","tag-jaume-luis-garcia-roig","tag-juan-gabriel-tena-ayuso","tag-lloreni-huguet-rotger","tag-merce-villanueva-gay","tag-t-phelps-kevin"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/13363","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=13363"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/13363\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=13363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=13363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=13363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}