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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2013, Volume 10, Pages 443–449 (Mi semr424)  
This article is cited in 1 scientific paper (total in 1 paper)

Discrete mathematics and mathematical cybernetics

Ranks of propelinear perfect binary codes

G. K. Guskova, I. Yu. Mogilnykhab, F. I. Solov'evaab

a Sobolev Institute of Mathematics, pr. ac. Koptyuga 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova street 2, 630090, Novosibirsk, Russia
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Abstract: It is proven that for any numbers $n=2^m-1, m\geq 4$ and $r$, such that $n-\log(n+1)\leq r \leq n$ excluding $n=r=63$, $n=127$, $r\in\{126,127\}$ and $n=r=2047$ there exists a propelinear perfect binary code of length $n$ and rank $r$.
Keywords: propelinear perfect binary codes, rank, transitive codes.
Received October 26, 2012, published May 22, 2013
Document Type: Article
UDC: 519.72
MSC: 94B25
Language: English
Citation: G. K. Guskov, I. Yu. Mogilnykh, F. I. Solov'eva, “Ranks of propelinear perfect binary codes”, Sib. Èlektron. Mat. Izv., 10 (2013), 443–449
Citation in format AMSBIB
\Bibitem{GusMogSol13}
\by G.~K.~Guskov, I.~Yu.~Mogilnykh, F.~I.~Solov'eva
\paper Ranks of propelinear perfect binary codes
\jour Sib. \`Elektron. Mat. Izv.
\yr 2013
\vol 10
\pages 443--449
\mathnet{http://mi.mathnet.ru/semr424}
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