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Problemy Peredachi Informatsii, 1975, Volume 11, Issue 3, Pages 3–13 (Mi ppi1590)  

This article is cited in 1 scientific paper (total in 2 paper)

Large Systems

Nonexistence of Perfect Codes for Some Composite Alphabets

L. A. Bassalygo, V. A. Zinov'ev, V. K. Leont'ev, N. I. Fel'dman
Full-text PDF (514 kB) Citations (2)
Abstract: It is known [V. A. Zinoviev and V. K. Leont'ev, Probl. Control Inf. Theory, 1973, vol. 2, no. 2, pp. 123–132; A. Tietäväinen, SIAM J. Appl. Math., 1973, vol. 24, no. 1, pp. 88–96] that if the cardinality of an alphabet $q$ is a power of a prime number, then nontrivial perfect codes other than the Hamming and Golay codes do not exist. A natural assumption is that this is true for composite $q$. In this paper it is shown that there do not exist nontrivial perfect codes over an alphabet of $q =2^{\alpha}3^{\beta}$ ($\alpha$,$\beta\geq l)$ symbols that correct $t\geq 2$ errors. The question remains an open one for $t=1$. The only known result in this case [S. W. Golomb and E. S. Posner, IEEE Trans. Inf. Theory, 1964, vol. 10, no. 1, pp. 196–208] is that a perfect single-error-correcting code does not exist for $q=6$ and $n=7$.
Received: 02.04.1974
Bibliographic databases:
Document Type: Article
UDC: 621.391.15:511
Language: Russian
Citation: L. A. Bassalygo, V. A. Zinov'ev, V. K. Leont'ev, N. I. Fel'dman, “Nonexistence of Perfect Codes for Some Composite Alphabets”, Probl. Peredachi Inf., 11:3 (1975), 3–13; Problems Inform. Transmission, 11:3 (1975), 181–189
Citation in format AMSBIB
\Bibitem{BasZinLeo75}
\by L.~A.~Bassalygo, V.~A.~Zinov'ev, V.~K.~Leont'ev, N.~I.~Fel'dman
\paper Nonexistence of Perfect Codes for Some Composite Alphabets
\jour Probl. Peredachi Inf.
\yr 1975
\vol 11
\issue 3
\pages 3--13
\mathnet{http://mi.mathnet.ru/ppi1590}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=490414}
\zmath{https://zbmath.org/?q=an:0326.94008}
\transl
\jour Problems Inform. Transmission
\yr 1975
\vol 11
\issue 3
\pages 181--189
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Проблемы передачи информации Problems of Information Transmission
     
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