Niemeier lattices and Type II codes over \(\mathbb{Z}_4\)

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)

zbMATH Keywords

even unimodular lattices\(Z_4\) codesextremal unimodular lattices

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Relations with coding theory (11H71)

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

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Double circulant codes over \(\mathbb{Z}_ 4\) and even unimodular lattices
• A group algebra construction of binary even self dual codes
• Selbstduale Codes über dem Ring der ganzen Zahlen modulo 4. (Self-dual codes over the ring of integers modulo 4)
• 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

This page was built for publication: Niemeier lattices and Type II codes over \(\mathbb{Z}_4\)