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Sib. Èlektron. Mat. Izv., 2011, Volume 8, Pages 372–380 (Mi semr336)  

Construction of partitions of the set of all $p$-ary vectors of length $p+1$ into Hamming codes

A. V. Los', K. I. Burnakov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We suggest the construction of a partition of the set of all $p$‑ary vectors of length $p+1$ into perfect $p$-ary codes, where $p$ is a prime. The construction yields the lower bound $N(p)>(e^{\pi\sqrt{2p/3}})/(4p\sqrt{3})$ on the number of nonequivalent such partitions for any prime $p$.

Keywords: perfect $q$-ary code, Hamming code, partition into codes, switchings.

Full text: PDF file (194 kB)
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UDC: 512.5
MSC: 13A99
Received November 18, 2011, published December 24, 2011

Citation: A. V. Los', K. I. Burnakov, “Construction of partitions of the set of all $p$-ary vectors of length $p+1$ into Hamming codes”, Sib. Èlektron. Mat. Izv., 8 (2011), 372–380

Citation in format AMSBIB
\Bibitem{LosBur11}
\by A.~V.~Los', K.~I.~Burnakov
\paper Construction of partitions of the set of all $p$-ary vectors of length $p+1$ into Hamming codes
\jour Sib. \`Elektron. Mat. Izv.
\yr 2011
\vol 8
\pages 372--380
\mathnet{http://mi.mathnet.ru/semr336}


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