{"id":5329,"date":"2025-06-30T13:12:34","date_gmt":"2025-06-30T13:12:34","guid":{"rendered":"https:\/\/fs.kibu.ac.ke\/?p=5329"},"modified":"2025-12-26T22:41:07","modified_gmt":"2025-12-26T22:41:07","slug":"binary-linear-codes-and-designs-from-the-orthogonal-group-o-82","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/fs\/binary-linear-codes-and-designs-from-the-orthogonal-group-o-82\/","title":{"rendered":"Binary Linear Codes and Designs from the Orthogonal Group O-8(2)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"5329\" class=\"elementor elementor-5329\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7e3ac6c4 elementor-section-full_width elementor-section-height-min-height elementor-section-items-stretch elementor-section-height-default\" data-id=\"7e3ac6c4\" data-element_type=\"section\" id=\"ourgoal\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-911faef\" data-id=\"911faef\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3561174e elementor-widget elementor-widget-theme-post-title elementor-page-title elementor-widget-heading\" data-id=\"3561174e\" data-element_type=\"widget\" data-widget_type=\"theme-post-title.default\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Binary Linear Codes and Designs from the Orthogonal Group O-8(2)<\/h1>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-14d58dcb elementor-section-height-min-height elementor-section-boxed elementor-section-height-default elementor-section-items-middle\" data-id=\"14d58dcb\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2677b825\" data-id=\"2677b825\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-1aa72195 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1aa72195\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-1b7bf93f elementor-invisible\" data-id=\"1b7bf93f\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b8dc351 elementor-widget__width-auto elementor-widget elementor-widget-heading\" data-id=\"b8dc351\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">2024<\/h2>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-23c0cfe6 elementor-invisible\" data-id=\"23c0cfe6\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-60f59426 elementor-widget elementor-widget-heading\" data-id=\"60f59426\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">KIBU Authors<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4f0caa87 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"4f0caa87\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Lucy Chikamai<\/p><p>Vincent Marani<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-5bea9c2 elementor-invisible\" data-id=\"5bea9c2\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-253be1ef elementor-tablet-align-left elementor-invisible elementor-widget elementor-widget-button\" data-id=\"253be1ef\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInLeft&quot;}\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-shrink\" href=\"https:\/\/www.irejournals.com\/paper-details\/1706061\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">VIEW ON PUBLISHER SITE<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-4b86a415 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4b86a415\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-34e2a0e0 elementor-invisible\" data-id=\"34e2a0e0\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4e544cb2 elementor-widget elementor-widget-heading\" data-id=\"4e544cb2\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4baf4245 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"4baf4245\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>This paper investigates the construction and analysis of binary linear codes and designs from the orthogonal group O?8(2). We employ the Key-Moori method and the modular theoretic approach to construct codes and designs from the primitive permutation representations of O?8(2) of degrees 119, 136, and 765. The study reveals the existence of optimal and near-optimal codes, as well as codes with desirable properties such as self-orthogonality and doubly-evenness. Connections between the codes and designs are explored, revealing interesting combinatorial structures. The findings contribute to the field of coding theory by providing new examples of codes with good parameters and to the understanding of the orthogonal group O?8(2) by revealing its rich submodule structure. The study also demonstrates the effectiveness of computational methods, such as MAGMA, in constructing and analyzing codes and designs from simple groups. Limitations and future research directions are discussed.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>2024 KIBU Authors Lucy Chikamai Vincent Marani VIEW ON PUBLISHER SITE Abstract This paper investigates the construction and analysis of binary linear codes and designs from the orthogonal group O?8(2). We employ the Key-Moori method and the modular theoretic approach to construct codes and designs from the primitive permutation representations of O?8(2) of degrees 119, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-5329","post","type-post","status-publish","format-standard","hentry","category-research-list"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Binary Linear Codes and Designs from the Orthogonal Group O-8(2) - Faculty of Science<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/kibu.ac.ke\/fs\/binary-linear-codes-and-designs-from-the-orthogonal-group-o-82\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Binary Linear Codes and Designs from the Orthogonal Group O-8(2) - Faculty of Science\" \/>\n<meta property=\"og:description\" content=\"2024 KIBU Authors Lucy Chikamai Vincent Marani VIEW ON PUBLISHER SITE Abstract This paper investigates the construction and analysis of binary linear codes and designs from the orthogonal group O?8(2). We employ the Key-Moori method and the modular theoretic approach to construct codes and designs from the primitive permutation representations of O?8(2) of degrees 119, [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/kibu.ac.ke\/fs\/binary-linear-codes-and-designs-from-the-orthogonal-group-o-82\/\" \/>\n<meta property=\"og:site_name\" content=\"Faculty of Science\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-30T13:12:34+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-26T22:41:07+00:00\" \/>\n<meta name=\"author\" content=\"kibabii\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"kibabii\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/binary-linear-codes-and-designs-from-the-orthogonal-group-o-82\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/binary-linear-codes-and-designs-from-the-orthogonal-group-o-82\/\"},\"author\":{\"name\":\"kibabii\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/#\/schema\/person\/fc9b7f13eeb65cf0be520197c35b17d6\"},\"headline\":\"Binary Linear Codes and Designs from the Orthogonal Group O-8(2)\",\"datePublished\":\"2025-06-30T13:12:34+00:00\",\"dateModified\":\"2025-12-26T22:41:07+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/binary-linear-codes-and-designs-from-the-orthogonal-group-o-82\/\"},\"wordCount\":160,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/#organization\"},\"articleSection\":[\"Research List\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/kibu.ac.ke\/fs\/binary-linear-codes-and-designs-from-the-orthogonal-group-o-82\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/binary-linear-codes-and-designs-from-the-orthogonal-group-o-82\/\",\"url\":\"https:\/\/kibu.ac.ke\/fs\/binary-linear-codes-and-designs-from-the-orthogonal-group-o-82\/\",\"name\":\"Binary Linear Codes and Designs from the Orthogonal Group O-8(2) - 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