References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

On the classification of perfect codes: Extended side class structuresPrimeFaces.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}); 2010 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 310, no 1, 43-55 p.Article in journal (Refereed) Published
##### Abstract [en]

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

2010. Vol. 310, no 1, 43-55 p.
##### Keyword [en]

Perfect codes, Side class structures, rank
##### Identifiers

URN: urn:nbn:se:kth:diva-19017DOI: 10.1016/j.disc.2009.07.023ISI: 000272437800007ScopusID: 2-s2.0-70350716446OAI: oai:DiVA.org:kth-19017DiVA: diva2:337064
#####

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#####

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#####

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##### Note

QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2012-01-31Bibliographically approved
##### In thesis

The two 1-error correcting perfect binary codes. C and C' are said to be equivalent if there exists a permutation pi of the set of the n coordinate positions and a word (d) over bar such that C' = pi((d) over bar + C). Hessler defined C and C' to be linearly equivalent if there exists a non-singular linear map phi such that C' = phi(C). Two perfect codes C and C' of length n will be defined to be extended equivalent if there exists a non-singular linear map W and a word (d) over bar such that C' = phi((d) over bar + C). Heden and Hessler, associated with each linear equivalence class an invariant L-C and this invariant was shown to be a subspace of the kernel of some perfect code. It is shown here that, in the case of extended equivalence, the corresponding invariant will be the extension of the code L-C. This fact will be used to give, in some particular cases, a complete enumeration of all extended equivalence classes of perfect codes.

1. Parity check systems, perfect codes and codes over Frobenius rings$(function(){PrimeFaces.cw("OverlayPanel","overlay484869",{id:"formSmash:j_idt731:0:j_idt735",widgetVar:"overlay484869",target:"formSmash:j_idt731:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});