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

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

Olof Heden 1, and  Faina I. Solov’eva 2,

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.
Keywords: Phelps partition., Perfect code, Hamming code, non-parallel Hamming codes.
Mathematics Subject Classification: Primary: 94B25, 94B60; Secondary: 94B0.
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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