Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-04T18:21:00.895Z Has data issue: false hasContentIssue false
  • English
  • Français

A construction of integral lattices

Published online by Cambridge University Press:  26 February 2010

H.-G. Quebbemann
H.-G. Quebbemann
Affiliation:
Mathematisches Institut der Universität, Einsteinstrasse 62, D-4400 Münster, West Germany.
Get access

Abstract

Given an integral lattice L and a hyperbolic decomposition of some quotient L/pL, there is a simple technique for obtaining other lattices of the same dimension and discriminant as L⊥ … ⊥L. When applied to the D4 and E8 root lattices, for example, this yields a new sphere packing in ℝ32, which is denser than those known up to now, and an extremal type II lattice in ℝ64.

Type
Research Article
Information
Mathematika , Volume 31 , Issue 1 , June 1984 , pp. 137 - 140
Copyright
Copyright © University College London 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Conway, J. H. and Sloane, N. J. A.. Laminated lattices. Annals of Math., 116 (1982), 593–620.CrossRefGoogle Scholar
2.Eichler, M.. Quadratische Formen und orthogonale Gruppen (Springer-Verlag, 1952).CrossRefGoogle Scholar
3.Leech, J. and Sloane, N. J. A.. Sphere packings and error-correcting codes. Canad. J. Math., 23 (1971), 718–745.CrossRefGoogle Scholar
4.Milnor, J. and Husemoller, D.. Symmetric bilinear forms (Springer-Verlag, 1973).CrossRefGoogle Scholar
5.Quebbemann, H.-G.. An application of Siegel's formula over quaternion orders. Mathematika, 31 (1984), 12–16.CrossRefGoogle Scholar
6.Sloane, N. J. A.. Binary codes, lattices and sphere packings. In Combinatorial Surveys (Proc. 6th British Combinatorial Conf.), ed. by Cameron, P. J. (Academic Press, 1977), 117–164.Google Scholar