Sphere Packings, Lattices and Groups

Front Matter....Pages i-xxvii
Sphere Packings and Kissing Numbers....Pages 1-30
Coverings, Lattices and Quantizers....Pages 31-62
Codes, Designs and Groups....Pages 63-93
Certain Important Lattices and Their Properties....Pages 94-135
Sphere Packing and Error-Correcting Codes....Pages 136-156
Laminated Lattices....Pages 157-180
Further Connections Between Codes and Lattices....Pages 181-205
Algebraic Constructions for Lattices....Pages 206-244
Bounds for Codes and Sphere Packings....Pages 245-266
Three Lectures on Exceptional Groups....Pages 267-298
The Golay Codes and The Mathieu Groups....Pages 299-330
A Characterization of the Leech Lattice....Pages 331-336
Bounds on Kissing Numbers....Pages 337-339
Uniqueness of Certain Spherical Codes....Pages 340-351
On the Classification of Integral Quadratic Forms....Pages 352-405
Enumeration of Unimodular Lattices....Pages 406-420
The 24-Dimensional Odd Unimodular Lattices....Pages 421-426
Even Unimodular 24-Dimensional Lattices....Pages 427-438
Enumeration of Extremal Self-Dual Lattices....Pages 439-442
Finding the Closest Lattice Point....Pages 443-448
Voronoi Cells of Lattices and Quantization Errors....Pages 449-475
A Bound for the Covering Radius of the Leech Lattice....Pages 476-477
The Covering Radius of the Leech Lattice....Pages 478-505
Twenty-Three Constructions for the Leech Lattice....Pages 506-512
The Cellular Structure of the Leech Lattice....Pages 513-521
Lorentzian Forms for the Leech Lattice....Pages 522-526
The Automorphism Group of the 26-Dimensional Lorentzian Lattice....Pages 527-531
Leech Roots and Vinberg Groups....Pages 532-553
The Monster Group and its 196884-Dimensional Space....Pages 554-567
A Monster Lie Algebra?....Pages 568-571
Back Matter....Pages 572-665