# American Institute of Mathematical Sciences

November  2009, 3(4): 385-397. doi: 10.3934/amc.2009.3.385

## Partitions of $\mathbb F$n into non-parallel Hamming codes

 1 Department of Mathematics, KTH, 10044 Stockholm, Sweden 2 Sobolev Institute of Mathematics, Novosibirsk State University, pr. ac. Koptyuga 4, Novosibirsk, 630090, Russian Federation

Received  June 2009 Revised  October 2009 Published  November 2009

We investigate partitions of the set $\mathbb F$n of all binary vectors of length $n$ into cosets of pairwise distinct linear Hamming codes (''non-parallel Hamming codes'') of length $n$. We present several constructions of partitions of $\mathbb F$n into non-parallel Hamming codes of length $n$ and discuss a lower bound on the number of different such partitions.
Citation: Olof Heden, Faina I. Solov’eva. Partitions of $\mathbb F$n into non-parallel Hamming codes. Advances in Mathematics of Communications, 2009, 3 (4) : 385-397. doi: 10.3934/amc.2009.3.385
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