CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt146",{id:"formSmash:upper:j_idt146",widgetVar:"widget_formSmash_upper_j_idt146",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt147_j_idt149",{id:"formSmash:upper:j_idt147:j_idt149",widgetVar:"widget_formSmash_upper_j_idt147_j_idt149",target:"formSmash:upper:j_idt147:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

ON THE EXISTENCE OF EXTENDED PERFECT BINARY CODES WITH TRIVIAL SYMMETRY GROUPPrimeFaces.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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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2009 (English)In: Advances in Mathematics of Communications, ISSN 1930-5346, Vol. 3, no 3, 295-309 p.Article in journal (Refereed) Published
##### Abstract [en]

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

2009. Vol. 3, no 3, 295-309 p.
##### Keyword [en]

Perfect codes, symmetry group, error-correcting codes, construction
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-18702DOI: 10.3934/amc.2009.3.295ISI: 000269220600007Scopus ID: 2-s2.0-69249097938OAI: oai:DiVA.org:kth-18702DiVA: diva2:336749
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt434",{id:"formSmash:j_idt434",widgetVar:"widget_formSmash_j_idt434",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt440",{id:"formSmash:j_idt440",widgetVar:"widget_formSmash_j_idt440",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt446",{id:"formSmash:j_idt446",widgetVar:"widget_formSmash_j_idt446",multiple:true});
##### Note

QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2012-02-01Bibliographically approved
##### In thesis

The set of permutations of the coordinate set that maps a perfect code C into itself is called the symmetry group of C and is denoted by Sym(C). It is proved that for all integers n = 2(m) - 1, where m = 4, 5, 6, ... , and for any integer r, where n - log(n + 1) + 3 <= r <= n - 1, there are perfect codes of length n and rank r with a trivial symmetry group, i.e. Sym(C) = {id}. The result is shown to be true, more generally, for the extended perfect codes of length n + 1.

1. Parity check systems, perfect codes and codes over Frobenius rings$(function(){PrimeFaces.cw("OverlayPanel","overlay484869",{id:"formSmash:j_idt707:0:j_idt711",widgetVar:"overlay484869",target:"formSmash:j_idt707:0: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_idt1197",{id:"formSmash:lower:j_idt1197",widgetVar:"widget_formSmash_lower_j_idt1197",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1198_j_idt1200",{id:"formSmash:lower:j_idt1198:j_idt1200",widgetVar:"widget_formSmash_lower_j_idt1198_j_idt1200",target:"formSmash:lower:j_idt1198:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});