The Leech Lattice and Conway Groups

1998 ◽  
pp. 95-103
Author(s):  
Robert L. Griess
Keyword(s):  
Leech Lattice

scholarly journals The theta functions of sublattices of the Leech lattice

1986 ◽  
Vol 101 ◽  
pp. 151-179 ◽  
Author(s):  
Takeshi Kondo ◽  
Takashi Tasaka
Keyword(s):  
Automorphism Group ◽  
Euclidean Space ◽  
Theta Functions ◽  
Orthogonal Basis ◽  
Permutation Representation ◽  
Dimensional Euclidean Space ◽  
Unimodular Lattice ◽  
Mathieu Group ◽  
Leech Lattice ◽  
Even Unimodular Lattice

Let Λ be the Leech lattice which is an even unimodular lattice with no vectors of squared length 2 in 24-dimensional Euclidean space R24. Then the Mathieu Group M24 is a subgroup of the automorphism group .0 of Λ and the action on Λ of M24 induces a natural permutation representation of M24 on an orthogonal basis For , let Λm be the sublattice of vectors invariant under m:

scholarly journals Z6-Code Constructions of the Leech Lattice and the Niemeier Lattices

2002 ◽  
Vol 23 (5) ◽  
pp. 573-581 ◽  
Author(s):  
Masaaki Harada ◽  
Masaaki Kitazume
Keyword(s):  
Leech Lattice ◽  
Code Constructions

scholarly journals Defining-relations for Hurwitz groups

1994 ◽  
Vol 36 (3) ◽  
pp. 363-370 ◽  
Author(s):  
C. M. Campbell ◽  
M. D. E. Conder ◽  
E. F. Robertson
Keyword(s):  
Sphere Packing ◽  
Computational Algebra ◽  
Leech Lattice ◽  
Defining Relations

With much sadness we note the death of John Leech, on 28 September 1992. Perhaps best known for his discovery of the “Leech Lattice” (which provides the best known sphere-packing in 24 dimensions), John will also be remembered for his contributions to the use of computers in mathematics, and to computational algebra in particular.

The Leech lattice and the Golay code: bounded-distance decoding and multilevel constructions

1994 ◽  
Vol 40 (4) ◽  
pp. 1030-1043 ◽  
Author(s):  
O. Amrani ◽  
Y. Be'ery ◽  
A. Vardy ◽  
Feng-Wen Sun ◽  
H.C.A. van Tilborg
Keyword(s):  
Golay Code ◽  
Leech Lattice ◽  
Bounded Distance
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