商品簡介
本書為第三版，繼前兩版之后，接著探討“如何最有效地將大量等球放入n維的歐氏空間中？”這一核心問題。同時，作者仍在思考一些相關的問題，如：吻接數問題，覆蓋問題，量子化問題以及格分類與二次型。與前兩版相同的是，第三版也描述了以上這些問題與數學或自然科學中其他一些領域的聯系，這些領域包括：碼理論，數字通信，數論，群論，模擬數字轉換以及數據壓縮與n維晶體。值得特別注意的是，本書收錄了一篇介紹本領域的最新的一些研究成果的報告，并補充了1988-1998年間出版的超過800項的參考書目，相信這些珍貴的資料一定能夠引起讀者特殊的興趣。本書適用于數學專業的高年級本科生或研究生以及需要相關知識的科研人員。
目次
Preface to First Edition
Preface to Third Edition
List of Symbols
Chapter 1 Sphere Packings and Kissing Numbers
Chapter 2 Coverings,Lattices and Quantizers
Chapter 3 Codes,Designs and Groups
Chapter 4 Certain Important Lattices and Their Properties
Chapter 5 Sphere Packing and Error-Correcting Codes
Chapter 6 Laminated Lattices
Chapter 7 Further Connections Betwwen Codes and Lattices
Chapter 8 Algebraic Constructions for Lattices
Chapter 9 Bounds for Codes and Sphere Packings
Chapter 10 Three Lectures on Exceptional Groups
Chapter 11 The Golay Codes and the Mathieu Groups
Chapter 12 A Characterization of the Leech Lattice
Chapter 13 Bounds on Kissing Numbers
Chapter 14 Uniqueness of Certain Spherical Codes
Chapter 15 On the Classification of Integral Quadratic Forms
Chapter 16 Enumeration of Unimodular Lattices
Chapter 17 The 24-Dimensional Odd Unimodular Lattices
Chapter 18 Even Unimodular 24-Dimensional Lattices
Chapter 19 Enumeration of Extremal Self-Dual Lattices
Chapter 20 Finding the Closest Lattice Point
Chapter 21 Voronoi Cells of Lattices and Quantization Errors
Chapter 22 A Bound for the Covering Radius of the Leech Lattice
Chapter 23 The Covering Radius of the Leech Lattice
Chapter 24 Twenty-Three Constructions for the Leech Lattice
Chapter 25 The Cellular Structure of the Leech Lattice
Chapter 26 Lorentzian Forms for the Leech Lattice
Chapter 27 The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian Lattice
Chapter 28 Leech Roots and Vinberg Groups
Chapter 29 The Monster Group and its 196884-Dimensional Space
Chapter 30 A Monster Lie Algebra?
Bibliography
Supplementary Bibliography
Index
