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

Olof Heden; Faina I. Solov’eva

doi:10.3934/amc.2009.3.385

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2009, Volume 3, Issue 4: 385-397. Doi: 10.3934/amc.2009.3.385

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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
2.
Sobolev Institute of Mathematics, Novosibirsk State University, pr. ac. Koptyuga 4, Novosibirsk, 630090

Received: May 31, 2009

Revised: September 30, 2009

Published: October 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 94B25, 94B60; Secondary: 94B05.

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