Niemeier lattices and Type II codes over \(\mathbb{Z}_4\)
type: Item
instance of: scholarly article
title: Niemeier lattices and Type II codes over \(\mathbb{Z}_4\)
zbMATH Open document ID: 1004.94025
DOI: 10.1016/S0012-365X(99)00032-1
author: Philippe Gaborit
author: Masaaki Harada
author: Masaaki Kitazume
author: Patrick Solé
author: Alexis Bonnecaze
published in: Discrete Mathematics
publication date: 2000-03-02T00:00:00Z
review text: The Leech lattice has previously been constructed from a self-dual code over the ring \(\mathbb{Z}_4\). There are 22 other even unimodular lattices in dimension 24. This paper shows that all of these lattices can be constructed from self-dual codes over \(\mathbb{Z}_4\). Generator matrices and symmetric weight enumerators are given for these codes. It is also shown that all extremal unimodular lattices can be constructed from self-dual codes over \(\mathbb{Z}_4\).
reviewed by: T. Aaron Gulliver
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 11H71
zbMATH DE Number: 1334673
zbMATH Keywords: \(Z_4\) codes
zbMATH Keywords: even unimodular lattices
zbMATH Keywords: extremal unimodular lattices
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1334673