Characteristic vectors of unimodular lattices which represent two
type: Item
instance of: scholarly article
title: Characteristic vectors of unimodular lattices which represent two
zbMATH Open document ID: 1216.11069
author: Mark Gaulter
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2008-07-21T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10804
review text: The author improves the known upper bound of the dimension \(n\) of an indecomposable unimodular lattice \(L\) whose shadow has the third largest possible length, \(s=n-16\) to \(n\leq 89\). \textit{G. Nebe} and \textit{B. Venkov} [J. Number Theory 99, No. 2, 307--317 (2003; Zbl 1081.11049)] proved that if \(L\) has no roots and \(s=n-16\), then \(\text{rank}(L)\leq 46\). This bound is attained by \(L=O_{23}\perp O_{23}\) where \(O_{23}\) is the shorter Leech lattice.
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 11H55
Mathematics Subject Classification ID: 11E12
zbMATH DE Number: 5302782
MaRDI profile type: Publication
OpenAlex ID: W1970166614
cites work: Q4039784
cites work: A characterization of the \(\mathbb Z^ n\) lattice
cites work: Lattices and codes with long shadows
cites work: A bound for certain \(s\)-extremal lattices and codes
cites work: Lattices without short characteristic vectors
cites work: Characteristic Elements of Unimodular -lattices
cites work: Euclidean lattices, spherical designs and modular forms. On the works of Boris Venkov
cites work: Unimodular lattices with long shadow
DOI: 10.5802/JTNB.594
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description: scientific article; zbMATH DE number 5302782