{"id":255,"date":"2021-11-15T13:31:30","date_gmt":"2021-11-15T06:31:30","guid":{"rendered":"https:\/\/conf.icgbio.ru\/lyap100\/?page_id=255"},"modified":"2021-11-17T14:11:42","modified_gmt":"2021-11-17T07:11:42","slug":"089-thesis","status":"publish","type":"page","link":"https:\/\/conf.icgbio.ru\/lyap100\/en\/reports\/089-thesis\/","title":{"rendered":"089. On the Steiner quadruple systems of small rank, embedded into perfect extended codes"},"content":{"rendered":"<p>It is well known that the set of all codewords of weight $4$ from any extended perfect code with the all-zero vector forms a Steiner quadruple system. In this paper it is shown that the Steiner quadruple system of order $2^t$ constructed by switchings from the Steiner quadruple system, corresponding to the Hamming code, is embedded into some extended perfect code constructed by switchings of $ijkl$-components from the binary extended Hamming code.<\/p>\n<p>&nbsp;<\/p>\n<table class=\"t-data-grid grid-top-border\">\n<tbody>\n<tr class=\"line1\">\n<td class=\"report-label\">Abstracts file:<\/td>\n<td class=\"report-text\"><a href=\"https:\/\/conf.icgbio.ru\/lyap100\/wp-content\/uploads\/sites\/82\/2021\/11\/lyap100-089-KovalSol_Theses.pdf\" target=\"_blank\" rel=\"noopener\">KovalSol_Theses.pdf<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>It is well known that the set of all codewords of weight $4$ from any extended perfect code with the all-zero vector forms a Steiner quadruple system. In this paper it is shown that the Steiner quadruple system of order &hellip; <a href=\"https:\/\/conf.icgbio.ru\/lyap100\/en\/reports\/089-thesis\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":13,"featured_media":0,"parent":58,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/conf.icgbio.ru\/lyap100\/en\/wp-json\/wp\/v2\/pages\/255"}],"collection":[{"href":"https:\/\/conf.icgbio.ru\/lyap100\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/conf.icgbio.ru\/lyap100\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/conf.icgbio.ru\/lyap100\/en\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/conf.icgbio.ru\/lyap100\/en\/wp-json\/wp\/v2\/comments?post=255"}],"version-history":[{"count":2,"href":"https:\/\/conf.icgbio.ru\/lyap100\/en\/wp-json\/wp\/v2\/pages\/255\/revisions"}],"predecessor-version":[{"id":903,"href":"https:\/\/conf.icgbio.ru\/lyap100\/en\/wp-json\/wp\/v2\/pages\/255\/revisions\/903"}],"up":[{"embeddable":true,"href":"https:\/\/conf.icgbio.ru\/lyap100\/en\/wp-json\/wp\/v2\/pages\/58"}],"wp:attachment":[{"href":"https:\/\/conf.icgbio.ru\/lyap100\/en\/wp-json\/wp\/v2\/media?parent=255"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}