On the existence of frames of the Niemeier lattices and self-dual codes over \(\mathbb F_p\)
type: Item
instance of: scholarly article
title: On the existence of frames of the Niemeier lattices and self-dual codes over \(\mathbb F_p\)
zbMATH Open document ID: 1189.11035
author: Masaaki Harada
published in: Journal of Algebra
publication date: 2009-06-17T00:00:00Z
review text: The Niemeier lattices are the 24 non-isomorphic 24-dimensional even unimodular lattices. Montague has shown that every Niemeier lattice can be constructed as an even unimodular neighbor of an odd unimodular lattice obtained from a self-dual code over \(F_3\) via construction A. The author proves that every Niemeier lattice can be constructed as an even unimodular neighbor of an odd unimodular lattice obtained from a self-dual code over \(F_p\) for each prime \(p\) with \(5 \leq p \leq 23\). A consequence is that every Niemeier lattice contains a \(2k\)-frame for \(k= 2, 3,\dots, 28\).
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 11H71
zbMATH DE Number: 5565635
zbMATH Keywords: Niemeier lattices
zbMATH Keywords: frame
zbMATH Keywords: self-dual code
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2009.02.001
OpenAlex ID: W2015607885
cites work: Niemeier lattices and Type II codes over \(\mathbb{Z}_4\)
cites work: Double circulant constructions of the Leech lattice
cites work: A note on optimal unimodular lattices
cites work: Q4219187
cites work: Q4241959
cites work: Orthogonal frames in the Leech lattice and a type II code over \(\mathbb{Z}_{22}\)
cites work: \(\mathbb Z_{6}\)-code constructions of the Leech lattice and the Niemeier lattices.
cites work: A new construction of lattices from codes over GF(3)
cites work: Q4878700
cites work: Definite quadratische Formen der Dimension 24 und Diskriminante 1
DOI: 10.1016/J.JALGEBRA.2009.02.001
description: scientific article; zbMATH DE number 5565635