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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

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

Perfect codes, Side class structures
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-51719DOI: 10.1016/j.disc.2009.07.023ISI: 000272437800007OAI: oai:DiVA.org:liu-51719DiVA: diva2:277119
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Available from: 2009-11-16 Created: 2009-11-16 Last updated: 2017-12-12Bibliographically approved
##### In thesis

The two 1-error correcting perfect binary codes, *C* and *C*^{′} are said to be equivalent if there exists a permutation *π* of the set of the *n* coordinate positions and a word such that . Hessler defined *C* and *C*^{′} to be linearly equivalent if there exists a non-singular linear map *φ* such that *C*^{′}=*φ*(*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 *φ* and a word such that

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. Optimization, Matroids and Error-Correcting Codes$(function(){PrimeFaces.cw("OverlayPanel","overlay277130",{id:"formSmash:j_idt707:0:j_idt711",widgetVar:"overlay277130",target:"formSmash:j_idt707:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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