On partitions of an $n$-cube into perfect binary codes

G. K. Guskov

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: A switching construction of partitions of an $n$-cube is studied. A new lower bound on the number of such partitions of rank that exceeds the rank of the Hamming code of the same length at most by 2 is established. Bibliogr. 17.

Keywords: perfect binary code, partition of an $n$-cube, rank of partition into perfect codes, lower bound on the number of partitions.

UDC: 519.8

Received: 27.04.2012
Revised: 04.02.2013

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