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Problemy Peredachi Informatsii, 1992, Volume 28, Issue 4, Pages 106–108
(Mi ppi1373)
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This article is cited in 1 scientific paper (total in 1 paper)
Сorrespondence
On Varshamov–Tenengolts Codes and a Conjecture of L. A. Bassalygo
D. M. Gevorkyan, G. A. Kabatiansky
Abstract:
We consider a construction problem for binary codes that correct single localized errors. L. A. Bassalygo stated a conjecture that the maximum “cardinality” (the number of messages) of such a code is equal to the integral part of the corresponding value of the Hamming bound. Using Varshamov–Tenengolts codes, we prove that this conjecture holds true for code length $n=p-1$, where $p$ is a prime such that 2 is its primitive root.
Received: 22.04.1991 Revised: 10.07.1992
Citation:
D. M. Gevorkyan, G. A. Kabatiansky, “On Varshamov–Tenengolts Codes and a Conjecture of L. A. Bassalygo”, Probl. Peredachi Inf., 28:4 (1992), 106–108; Problems Inform. Transmission, 28:4 (1992), 393–395
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https://www.mathnet.ru/eng/ppi1373 https://www.mathnet.ru/eng/ppi/v28/i4/p106
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