Niemeier lattice[1]
Description
One of the 24 positive-definite even unimodular lattices of rank 24.Cousins
- Self-dual linear code— The nine inequivalent \([24,12]\) doubly even self-dual codes [2] yield certain Niemeier lattices via Construction A [3]. Niemeier lattices can be constructed from ternary self-dual codes of length 24 [4].
- Self-dual code over \(\mathbb{Z}_q\)— Extremal Type II self-dual codes of length 24 over \(\mathbb{Z}_6\) yield Niemeier lattices [5].
- Harada-Kitazume code— Niemeier lattices can be constructed from quaternary codes over \(\mathbb{Z}_4\) via Construction \(A_4\) [6]. These codes are the Harada-Kitazume codes [3].
Member of code lists
Primary Hierarchy
Parents
Niemeier lattices are even and unimodular.
Niemeier lattices can be constructed from quaternary codes over \(\mathbb{Z}_4\) via Construction \(A_4\) [6]. These codes are the Harada-Kitazume codes [3].
Niemeier lattice
Children
References
- [1]
- H.-V. Niemeier, “Definite quadratische formen der dimension 24 und diskriminante 1”, Journal of Number Theory 5, 142 (1973) DOI
- [2]
- V. Pless and N. J. A. Sloane, “On the classification and enumeration of self-dual codes”, Journal of Combinatorial Theory, Series A 18, 313 (1975) DOI
- [3]
- M. Harada and M. Kitazume, “Z4-Code Constructions for the Niemeier Lattices and their Embeddings in the Leech Lattice”, European Journal of Combinatorics 21, 473 (2000) DOI
- [4]
- P. S. Montague, “A new construction of lattices from codes over GF(3)”, Discrete Mathematics 135, 193 (1994) DOI
- [5]
- M. Harada and M. Kitazume, “Z6-Code Constructions of the Leech Lattice and the Niemeier Lattices”, European Journal of Combinatorics 23, 573 (2002) DOI
- [6]
- 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
- [7]
- C. Dong, H. Li, G. Mason, and S. P. Norton, “Associative subalgebras of the Griess algebra and related topics”, (1996) arXiv:q-alg/9607013
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