G. K. Guskov, I. Yu. Mogilnykh, F. I. Solov'eva, “Ranks of propelinear perfect binary codes”, Sib. Èlektron. Mat. Izv., 2013, Volume 10,Pages <nobr>443

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Discrete mathematics and mathematical cybernetics

Ranks of propelinear perfect binary codes

G. K. Guskov^a, I. Yu. Mogilnykh^ab, F. I. Solov'eva^ab

^a Sobolev Institute of Mathematics, pr. ac. Koptyuga 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova street 2, 630090, Novosibirsk, Russia

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.

UDC: 519.72

MSC: 94B25

Received October 26, 2012, published May 22, 2013

Language: English