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The non-existence of some perfect codes over non-prime power alphabets
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2011 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 311, no 14, 1344-1348 p.Article in journal (Refereed) Published
Abstract [en]

Let exp(p)(q) denote the number of times the prime number p appears in the prime factorization of the integer q. The following result is proved: If there is a perfect 1-error correcting code of length n over an alphabet with q symbols then, for every prime number p. exp(p)(1 + n(q - 1)) <= exp(p)(q)(1 + (n - 1)/q). This condition is stronger than both the packing condition and the necessary condition given by the Lloyd theorem, as it for example excludes the existence of a perfect code with the parameters (n q, e) = (19, 6. 1).

Place, publisher, year, edition, pages
2011. Vol. 311, no 14, 1344-1348 p.
Keyword [en]
Perfect codes
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-35138DOI: 10.1016/j.disc.2011.03.024ISI: 000291283800009Scopus ID: 2-s2.0-79955588769OAI: oai:DiVA.org:kth-35138DiVA: diva2:426117
Note
QC 20110622Available from: 2011-06-22 Created: 2011-06-20 Last updated: 2017-12-11Bibliographically approved

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