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Niemeier lattice[1]

Description

One of the 24 positive-definite even unimodular lattices of rank 24.

Cousins

Member of code lists

Primary Hierarchy

Classical Domain
Analog Kingdom
Analog codeECC
Sphere packing
Lattice-based codeECC
Dual lattice
Unimodular lattice
Parents
Unimodular lattice
Niemeier lattices are even and unimodular.
Niemeier lattice
Children
\(\Lambda_{24}\) Leech lattice

References

[1]
H.-V. Niemeier, “Definite quadratische formen der dimension 24 und diskriminante 1”, Journal of Number Theory 5, 142 (1973) DOI
[2]
P. S. Montague, “A new construction of lattices from codes over GF(3)”, Discrete Mathematics 135, 193 (1994) DOI
[3]
A. Bonnecaze, P. Gaborit, M. Harada, M. Kitazume, and P. Solé, “Niemeier lattices and Type II codes over Z4”, Discrete Mathematics 205, 1 (1999) DOI
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Zoo Code ID: niemeier

Cite as:
“Niemeier lattice”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/niemeier
BibTeX:
@incollection{eczoo_niemeier, title={Niemeier lattice}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/niemeier} }
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Permanent link:
https://errorcorrectionzoo.org/c/niemeier

Cite as:

“Niemeier lattice”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/niemeier

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/analog/lattice/niemeier.yml.