Niemeier lattice[1]
Description
One of the 24 positive-definite even unimodular lattices of rank 24.
Parent
- Unimodular lattice — Niemeier lattice codes are even and unimodular.
Child
Cousins
- Self-dual linear code — Niemeier lattice codes can be constructed from ternary self-dual codes of length 24 [2].
- Quaternary linear code over \(\mathbb{Z}_4\) — Niemeier lattice codes can be constructed from quaternary codes over \(\mathbb{Z}_4\) via Construction \(A_4\) [3].
- Octacode — The octacode can be used to construct a Niemeier lattice code via Construction \(A_4\) [3].
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
Page edit log
- Victor V. Albert (2022-11-08) — most recent
Cite as:
“Niemeier lattice”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/niemeier