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Problemy Peredachi Informatsii, 1975, Volume 11, Issue 3, Pages 3–13
(Mi ppi1590)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/ppi1590 https://www.mathnet.ru/eng/ppi/v11/i3/p3
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