CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt187",{id:"formSmash:upper:j_idt187",widgetVar:"widget_formSmash_upper_j_idt187",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt189_j_idt191",{id:"formSmash:upper:j_idt189:j_idt191",widgetVar:"widget_formSmash_upper_j_idt189_j_idt191",target:"formSmash:upper:j_idt189:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

on the symmetry group of extended perfect binary codes of length n+1 and rank n-log(n+1)+2PrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2012 (English)In: Advances in Mathematics of Communication, ISSN 1930-5346, Vol. 6, no 2, p. 121-130Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2012. Vol. 6, no 2, p. 121-130
##### Keywords [en]

Perfect codes, symmetry group
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-71321DOI: 10.3934/amc.2012.6.121ISI: 000304194500001Scopus ID: 2-s2.0-84861967067OAI: oai:DiVA.org:kth-71321DiVA, id: diva2:486653
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt685",{id:"formSmash:j_idt685",widgetVar:"widget_formSmash_j_idt685",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt694",{id:"formSmash:j_idt694",widgetVar:"widget_formSmash_j_idt694",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt706",{id:"formSmash:j_idt706",widgetVar:"widget_formSmash_j_idt706",multiple:true});
##### Funder

Knut and Alice Wallenberg Foundation, KAW 2005.0098
##### Note

QC 20120612Available from: 2012-01-31 Created: 2012-01-31 Last updated: 2012-06-12Bibliographically approved
##### In thesis

It is proved that for every integer n = 2(k) - 1, with k >= 5, there exists a perfect code C of length n, of rank r = n - log(n + 1) + 2 and with a trivial symmetry group. This result extends an earlier result by the authors that says that for any length n = 2(k) - 1, with k >= 5, and any rank r, with n - log(n + 1) + 3 <= r <= n - 1 there exist perfect codes with a trivial symmetry group.

1. Parity check systems, perfect codes and codes over Frobenius rings$(function(){PrimeFaces.cw("OverlayPanel","overlay484869",{id:"formSmash:j_idt1419:0:j_idt1430",widgetVar:"overlay484869",target:"formSmash:j_idt1419:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt2094",{id:"formSmash:lower:j_idt2094",widgetVar:"widget_formSmash_lower_j_idt2094",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt2095_j_idt2097",{id:"formSmash:lower:j_idt2095:j_idt2097",widgetVar:"widget_formSmash_lower_j_idt2095_j_idt2097",target:"formSmash:lower:j_idt2095:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});