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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.
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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

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References

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