Niemeier lattices and Type II codes over \(\mathbb{Z}_4\)
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Publication:1301825
DOI10.1016/S0012-365X(99)00032-1zbMath1004.94025MaRDI QIDQ1301825
Philippe Gaborit, Patrick Solé, Masaaki Harada, Masaaki Kitazume, Alexis Bonnecaze
Publication date: 2 March 2000
Published in: Discrete Mathematics (Search for Journal in Brave)
Related Items (5)
A DETAILED STUDY OF THE RELATIONSHIP BETWEEN SOME OF THE ROOT LATTICES AND THE CODING THEORY ⋮ On the existence of frames of the Niemeier lattices and self-dual codes over \(\mathbb F_p\) ⋮ Covering aspects of the Niemeier lattices ⋮ \(\mathbb{Z}_4\)-code constructions for the Niemeier lattices and their embeddings in the Leech lattice ⋮ \(\mathbb Z_{6}\)-code constructions of the Leech lattice and the Niemeier lattices.
Cites Work
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- Double circulant codes over \(\mathbb{Z}_ 4\) and even unimodular lattices
- A group algebra construction of binary even self dual codes
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- Self-dual codes over the integers modulo 4
- Cyclic self-dual \(\mathbb Z_4\)-codes.
- A new construction of lattices from codes over GF(3)
- New extremal type II codes over \(\mathbb{Z}_4\)
- Definite quadratische Formen der Dimension 24 und Diskriminante 1
- A permutation decoding of the (24, 12, 8) Golay code (Corresp.)
- Extremal self‐dual lattices exist only in dimensions 1 to 8, 12, 14, 15, 23, and 24
- Type II codes over Z/sub 4/
- All self-dual Z/sub 4/ codes of length 15 or less are known
- Quaternary quadratic residue codes and unimodular lattices
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