On the classification of perfect codes: Extended side class structures
2010 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 310, no 1, 43-55 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2010. Vol. 310, no 1, 43-55 p.
Perfect codes, Side class structures, rank
IdentifiersURN: 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
QC 201005252010-08-052010-08-052012-01-31Bibliographically approved