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A remark on full rank perfect codes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2006 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 306, no 16, 1975-1980 p.Article in journal (Refereed) Published
Abstract [en]

Any full rank perfect 1-error correcting binary code of length n = 2(k) - 1 and with a kernel of dimension n - log(n + 1) - m, where in is sufficiently large, may be used to construct a full rank perfect 1-error correcting binary code of length 2(m) - 1 and with a kernel of dimension n - log(n + 1) - k. Especially we may construct full rank perfect 1-error correcting binary codes of length n = 2(m) - 1 and with a kernel of dimension n - log(n + 1) - 4 for nt = 6, 7,..., 10. This result extends known results on the possibilities for the size of a kernel of a full rank perfect code.

Place, publisher, year, edition, pages
2006. Vol. 306, no 16, 1975-1980 p.
Keyword [en]
perfect codes, super dual, tiling, tilings
Identifiers
URN: urn:nbn:se:kth:diva-15955DOI: 10.1016/j.disc.2006.02.014ISI: 000240173300017Scopus ID: 2-s2.0-33746772682OAI: oai:DiVA.org:kth-15955DiVA: diva2:333997
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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