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

J. H. Conway, A. M. Odlyzko, N. J.A. Sloane

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

It is known that if Λ is a self-dual lattice in ℝn, then min {u·u ǀ u ∈ Λ, u ≠ 0} ≤ [n/8] + 1. 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.

Original languageEnglish (US)
Pages (from-to)36-43
Number of pages8
JournalMathematika
Volume25
Issue number1
DOIs
StatePublished - Jan 1 1978

Fingerprint

Dive into the research topics of 'Extremal self-dual lattices exist only in dimensions 1 to 8, 12, 14, 15, 23, and 24'. Together they form a unique fingerprint.

Cite this