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On rank and kernel of some mixed perfect codes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2009 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 309, no 9, 2763-2774 p.Article in journal (Refereed) Published
Abstract [en]

Mixed perfect 1-error correcting codes and the associated dual codes over the group Z (n, l), Z (n, l) = under(under(Z2 × Z2 × ⋯ × Z2, {presentation form for vertical right curly bracket}), n) × underover(Z, 2, l), n ≥ 1 and l ≥ 2, are investigated. A lower and an upper bound for the rank k of the kernel of mixed perfect 1-error correcting codes in Z (n, l), depending on the rank r of the mixed perfect code and the structure of the corresponding dual code, are given. Due to a general construction of mixed perfect 1-error correcting group codes in Z (n, l), we show that the upper bound is tight for some n, l and r.

Place, publisher, year, edition, pages
2009. Vol. 309, no 9, 2763-2774 p.
Keyword [en]
Mixed perfect code, Rank, Fourier coefficient
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-32559DOI: 10.1016/j.disc.2008.06.037ISI: 000266541200016Scopus ID: 2-s2.0-67349187685OAI: oai:DiVA.org:kth-32559DiVA: diva2:411023
Note
QC 20110415Available from: 2011-04-15 Created: 2011-04-15 Last updated: 2017-12-11Bibliographically approved

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