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

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


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