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Sphere Packings, Lattices and Groups

  • Book
  • © 1993

Overview

Authors:
  1. J. H. Conway

    1. Mathematics Department, Princeton University, Princeton, USA

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    You can also search for this author in PubMed   Google Scholar

  2. N. J. A. Sloane

    1. Mathematical Sciences Research Center, AT&T Bell Laboratories, Murray Hill, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 290)

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Table of contents (30 chapters)

  1. Front Matter

    Pages i-xliii
    Download chapter PDF

  2. Sphere Packings and Kissing Numbers

    • J. H. Conway, N. J. A. Sloane
    Pages 1-30

  3. Coverings, Lattices and Quantizers

    • J. H. Conway, N. J. A. Sloane
    Pages 31-62

  4. Codes, Designs and Groups

    • J. H. Conway, N. J. A. Sloane
    Pages 63-93

  5. Certain Important Lattices and Their Properties

    • J. H. Conway, N. J. A. Sloane
    Pages 94-135

  6. Sphere Packing and Error-Correcting Codes

    • John Leech, N. J. A. Sloane
    Pages 136-156

  7. Laminated Lattices

    • J. H. Conway, N. J. A. Sloane
    Pages 157-180

  8. Further Connections Between Codes and Lattices

    • N. J. A. Sloane
    Pages 181-205

  9. Algebraic Constructions for Lattices

    • J. H. Conway, N. J. A. Sloane
    Pages 206-244

  10. Bounds for Codes and Sphere Packings

    • N. J. A. Sloane
    Pages 245-266

  11. Three Lectures on Exceptional Groups

    • J. H. Conway
    Pages 267-298

  12. The Golay Codes and The Mathieu Groups

    • J. H. Conway
    Pages 299-330

  13. A Characterization of the Leech Lattice

    • J. H. Conway
    Pages 331-336

  14. Bounds on Kissing Numbers

    • A. M. Odlyzko, N. J. A. Sloane
    Pages 337-339

  15. Uniqueness of Certain Spherical Codes

    • E. Bannai, N. J. A. Sloane
    Pages 340-351

  16. On the Classification of Integral Quadratic Forms

    • J. H. Conway, N. J. A. Sloane
    Pages 352-405

  17. Enumeration of Unimodular Lattices

    • J. H. Conway, N. J. A. Sloane
    Pages 406-420

  18. The 24-Dimensional Odd Unimodular Lattices

    • R. E. Borcherds
    Pages 421-426

  19. Even Unimodular 24-Dimensional Lattices

    • B. B. Venkov
    Pages 427-438

  20. Enumeration of Extremal Self-Dual Lattices

    • J. H. Conway, A. M. Odlyzko, N. J. A. Sloane
    Pages 439-442
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About this book

The second edition of this timely, 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 continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics. Results as of 1992 have been added to the text, and the extensive bibliography - itself a contribution to the field - is supplemented with approximately 450 new entries.

Authors and Affiliations

  • Mathematics Department, Princeton University, Princeton, USA

    J. H. Conway

  • Mathematical Sciences Research Center, AT&T Bell Laboratories, Murray Hill, USA

    N. J. A. Sloane

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