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Perfect codes as isomorphic spaces
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2006 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 306, no 16, 1981-1987 p.Article in journal (Refereed) Published
Abstract [en]

Linear equivalence between perfect codes is defined. This definition gives the concept of general perfect 1-error correcting binary codes. These are defined as 1-error correcting perfect binary codes, with the difference that the set of errors is not the set of weight one words, instead any set with cardinality n and full rank is allowed. The side class structure defines the restrictions on the subspace of any general 1-error correcting perfect binary code. Every linear equivalence class will contain all codes with the same length, rank and dimension of kernel and all codes in the linear equivalence class will have isomorphic side class structures.

Place, publisher, year, edition, pages
2006. Vol. 306, no 16, 1981-1987 p.
Keyword [en]
perfect codes, dual codes, classification
National Category
URN: urn:nbn:se:kth:diva-37592DOI: 10.1016/j.disc.2006.03.039ISI: 000240173300018ScopusID: 2-s2.0-33746722007OAI: diva2:434361
Available from: 2011-08-15 Created: 2011-08-15 Last updated: 2011-08-15Bibliographically approved

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