Tiling Hamming space with few spheres (Q1374207)
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scientific article; zbMATH DE number 1093117
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Tiling Hamming space with few spheres |
scientific article; zbMATH DE number 1093117 |
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Tiling Hamming space with few spheres (English)
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2 December 1997
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A binary generalized perfect code is a partition of \(\mathbb F^n_2\) into \(M\) spheres (or better: balls) with possibly different radii. It is shown that for such a partition, either \(M\leq 2\) (trivial cases) or \(M\geq n+2\). If \(M=n+2\), then one of the spheres has radius \(n-2\) and all others consist of one point. The proof depends on the well-known De Bruijn-Erdös theorem on the number of lines in a linear space.
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tiling
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Haming space
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generalized Steiner system
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generalized perfect code
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