Items related to Sphere Packings, Lattices and Groups
Synopsis
1 Sphere Packings and Kissing Numbers.- 2 Coverings, Lattices and Quantizers.- 3 Codes, Designs and Groups.- 4 Certain Important Lattices and Their Properties.- 5 Sphere Packing and Error-Correcting Codes.- 6 Laminated Lattices.- 7 Further Connections Between Codes and Lattices.- 8 Algebraic Constructions for Lattices.- 9 Bounds for Codes and Sphere Packings.- 10 Three Lectures on Exceptional Groups.- 11 The Golay Codes and the Mathieu Groups.- 12 A Characterization of the Leech Lattice.- 13 Bounds on Kissing Numbers.- 14 Uniqueness of Certain Spherical Codes.- 15 On the Classification of Integral Quadratic Forms.- 16 Enumeration of Unimodular Lattices.- 17 The 24-Dimensional Odd Unimodular Lattices.- 18 Even Unimodular 24-Dimensional Lattices.- 19 Enumeration of Extremal Self-Dual Lattices.- 20 Finding the Closest Lattice Point.- 21 Voronoi Cells of Lattices and Quantization Errors.- 22 A Bound for the Covering Radius of the Leech Lattice.- 23 The Covering Radius of the Leech Lattice.- 24 Twenty-Three Constructions for the Leech Lattice.- 25 The Cellular Structure of the Leech Lattice.- 26 Lorentzian Forms for the Leech Lattice.- 27 The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian Lattice.- 28 Leech Roots and Vinberg Groups.- 29 The Monster Group and its 196884-Dimensional Space.- 30 A Monster Lie Algebra?.- Supplementary Bibliography.
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