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.

UDC: 512.5

MSC: 13A99

Received November 18, 2011, published December 24, 2011