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Perfect codes from the dual point of view I
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2008 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 308, no 24, 6141-6156 p.Article in journal (Refereed) Published
Abstract [en]

The two concepts dual code and parity check matrix for a linear perfect 1-error correcting binary code are generalized to the case of non-linear perfect codes. We show how this generalization can be used to enumerate some particular classes of perfect 1-error correcting binary codes. We also use it to give an answer to a problem of Avgustinovich: whether or not the kernel of every perfect 1-error correcting binary code is always contained in some Hamming code.

Place, publisher, year, edition, pages
2008. Vol. 308, no 24, 6141-6156 p.
Keyword [en]
Perfect codes, error-correcting codes, rank
Identifiers
URN: urn:nbn:se:kth:diva-18014DOI: 10.1016/j.disc.2007.11.037ISI: 000261259100025Scopus ID: 2-s2.0-56649123449OAI: oai:DiVA.org:kth-18014DiVA: diva2:336059
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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