TY - JOUR
T1 - Extremal self-dual lattices exist only in dimensions 1 to 8, 12, 14, 15, 23, and 24
AU - Conway, J. H.
AU - Odlyzko, A. M.
AU - Sloane, N. J.A.
PY - 1978
Y1 - 1978
N2 - 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.
AB - 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.
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U2 - 10.1112/S0025579300009244
DO - 10.1112/S0025579300009244
M3 - Article
AN - SCOPUS:0242343336
SN - 0025-5793
VL - 25
SP - 36
EP - 43
JO - Mathematika
JF - Mathematika
IS - 1
ER -