\(\mathbb Z_{6}\)-code constructions of the Leech lattice and the Niemeier lattices. (Q1864573)
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scientific article; zbMATH DE number 1884145
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\mathbb Z_{6}\)-code constructions of the Leech lattice and the Niemeier lattices. |
scientific article; zbMATH DE number 1884145 |
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\(\mathbb Z_{6}\)-code constructions of the Leech lattice and the Niemeier lattices. (English)
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18 March 2003
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A self-dual code over \(\mathbb Z_{2k}\) is said to be of type II if all its words have Euclidean weight divisible by \(4k\). The authors consider the case \(k=3\) and construct such codes with length 24 and (extremal) minimal norm 24, by using an arbitrary type II binary self-dual code and an extremal ternary self-dual code of length 24. Also connections with the Leech lattice and with the Niemeier lattices are discussed.
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extremal code
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Leech lattice
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Niemeier lattice
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