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Extremal self-dual lattices exist only in dimensions 1 to 8, 12, 14, 15, 23, and 24

Published online by Cambridge University Press:  26 February 2010

J. H. Conway ,
A. M. Odlyzko  and
N. J. A. Sloane
J. H. Conway
Affiliation:
University of Cambridge, Cambridge, England.
A. M. Odlyzko
Affiliation:
Bell Laboratories, Murray Hill, New Jersey, 07974, U.S.A
N. J. A. Sloane
Affiliation:
Bell Laboratories, Murray Hill, New Jersey, 07974, U.S.A
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Abstract

It is known that if Λ is a self-dual lattice in ℝn, then

.

If equality holds the lattice is called extremal. In this paper we find all the extremal lattices: there are unique lattices in dimensions 1, 2, 3, 4, 5, 6, 7, 8, 12, 14, 15, 23, 24 and no others.

Type
Research Article
Information
Mathematika , Volume 25 , Issue 1 , June 1978 , pp. 36 - 43
Copyright
Copyright © University College London 1978

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