Sphere Packings, Lattices and Groups

By: John Conway, Neil J. A. Sloane

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Hardcover | 7 December 1998 | Edition Number 3

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Hardcover
788 Pages

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Revised

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16.6 x 24.2 x 4.8

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The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.

Industry Reviews

Third Edition

J.H. Conway and N.J.A. Sloane

Sphere Packings, Lattices and Groups

"This is the third edition of this reference work in the literature on sphere packings and related subjects. In addition to the content of the preceding editions, the present edition provides in its preface a detailed survey on recent developments in the field, and an exhaustive supplementary bibliography for 1988-1998. A few chapters in the main text have also been revised."--MATHEMATICAL REVIEWS

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Preface to First Edition
Preface to Third Edition
List of Symbols
Sphere Packings and Kissing Numbers	p. 1
Coverings, Lattices and Quantizers	p. 31
Codes, Designs and Groups	p. 63
Certain Important Lattices and Their Properties	p. 94
Sphere Packing and Error-Correcting Codes	p. 136
Laminated Lattices	p. 157
Further Connections Between Codes and Lattices	p. 181
Algebraic Constructions for Lattices	p. 206
Bounds for Codes and Sphere Packings	p. 245
Three Lectures on Exceptional Groups	p. 267
The Golay Codes and the Mathieu Groups	p. 299
A Characterization of the Leech Lattice	p. 331
Bounds on Kissing Numbers	p. 337
Uniqueness of Certain Spherical Codes	p. 340
On the Classification of Integral Quadratic Forms	p. 352
Enumeration of Unimodular Lattices	p. 406
The 24-Dimensional Odd Unimodular Lattices	p. 421
Even Unimodular 24-Dimensional Lattices	p. 429
Enumeration of Extremal Self-Dual Lattices	p. 441
Finding the Closest Lattice Point	p. 445
Voronoi Cells of Lattices and Quantization Errors	p. 451
A Bound for the Covering Radius of the Leech Lattice	p. 478
The Covering Radius of the Leech Lattice	p. 480
Twenty-Three Constructions for the Leech Lattice	p. 508
The Cellular Structure of the Leech Lattice	p. 515
Lorentzian Forms for the Leech Lattice	p. 524
The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian Lattice	p. 529
Leech Roots and Vinberg Groups	p. 534
The Monster Group and its 196884-Dimensional Space	p. 556
A Monster Lie Algebra?	p. 570
Bibliography	p. 574
Supplementary Bibliography	p. 642
Index	p. 681
Table of Contents provided by Blackwell. All Rights Reserved.

Sphere Packings, Lattices and Groups

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