图书信息

作者简介

内容简介

目录

图书信息

出版社: 世界图书出版公司; 第3版 (2008年11月1日)

平装: 703页

正文语种: 英语

开本: 24

ISBN: 9787506292153

条形码: 9787506292153

尺寸: 22.2 x 15 x 3.2 cm

重量: 939 g

作者简介

作者：(英国)康韦 (Conway.J.H)

内容简介

《球垛格点和群(第3版)》,继前两版之后，接着探讨“如何最有效地将大量等球放入n维的欧氏空间中？”这一核心问题。同时，作者仍在思考一些相关的问题，如：吻接数问题，覆盖问题，量子化问题以及格分类与二次型。与前两版相同的是，第三版也描述了以上这些问题与数学或自然科学中其他一些领域的联系，这些领域包括：码理论，数字通信，数论，群论，模拟数字转换以及数据压缩与n维晶体。值得特别注意的是，《球垛格点和群(第3版)》收录了一篇介绍本领域的最新的一些研究成果的报告，并补充了1988-1998年间出版的超过800项的参考书目，相信这些珍贵的资料一定能够引起读者特殊的兴趣。《球垛格点和群(第3版)》适用于数学专业的高年级本科生或研究生以及需要相关知识的科研人员。

目录

Preface to First Edition

Preface to Third Edition

List of Symbols

Chapter 1

Sphere Packings and Kissing Numbers

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

1. The Sphere Packing Problem

1.1 Packing Ball Bearings

1.2 Lattice Packings

1.3 Nonlattice Packings

1.4 n-Dimensional Packings

1.5 Sphere Packing Problem-Summary of Results

2. The Kissing Number Problem

2.1 The Problem of the Thirteen Spheres

2.2 Kissing Numbers in Other Dimensions

2.3 Spherical Codes

2.4 The Construction of Spherical Codes from Sphere Packings

2.5 The Construction of Spherical Codes from Binary Codes

2.6 Bounds on A(n,)

Appendix: Planetary Perturbations

Chapter 2

Coverings, Lattices and Quantizers

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

1. The Covering Problem

1.1 Covering Space with Overlapping Spheres

1.2 The Covering Radius and the Voronoi Cells

1.3 Covering Problem-Summary of Results

1.4 Computational Difficulties in Packings and Coverings

2. Lattices, Quadratic Forms and Number Theory

2.1 The Norm of a Vector

2.2 Quadratic Forms Associated with a Lattice

2.3 Theta Series and Connections with Number Theory

2.4 Integral Lattices and Quadratic Forms

2.5 Modular Forms

2.6 Complex and Quaternionic Lattices

3. Quantizers

3.1 Quantization, Analog-to-Digital Conversion and Data Compression

3.2 The Quantizer Problem

3.3 Quantizer Problem-Summary of Results

Chapter 3

Codes, Designs and Groups

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

1. The Channel Coding Problem

1.1 The Sampling Theorem

1.2 Shannon's Theorem

1.3 Error Probability

1.4 Lattice Codes for the Gaussian Channel

2. Error-Correcting Codes

2.1 The Error-Correcting Code Problem

2.2 Further Definitions from Coding Theory

2.3 Repetition, Even Weight and Other Simple Codes

2.4 Cyclic Codes

2.5 BCH and Reed-Solomon Codes

2.6 Justesen Codes

2.7 Reed-Muller Codes

2.8 Quadratic Residue Codes

2.9 Perfect Codes

2.10 The Pless Double Circulant Codes

2.11 Goppa Codes and Codes from Algebraic Curves

2.12 Nonlinear Codes

2.13 Hadamard Matrices

3. t-Designs, Steiner Systems and Spherical t-Designs

3.1 t-Designs and Steiner Systems

3.2 Spherical t-Designs

4. The Connections with Group Theory

4.1 The Automorphism Group of a Lattice

4.2 Constructing Lattices and Codes from Groups

Chapter 4

Certain Important Lattices and Their Properties

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

1. Introduction

2. Reflection Groups and Root Lattices

3. Gluing Theory

4. Notation; Theta Functions

4.1 Jacobi Theta Functions

5. The n-Dimensional Cubic Lattice Zn .

6. The n-Dimensional Lattices An and An*

6.1 The Lattice An.

6.2 The Hexagonal Lattice

6.3 The Face-Centered Cubic Lattice

6.4 The Tetrahedral or Diamond Packing

6.5 The Hexagonal Close-Packing

6.6 The Dual Lattice A*

6.7 The Body-Centered Cubic Lattice

7. The n-Dimensional Lattices Dn and Dn*

7.1 The Lattice Dn.

7.2 The Four-Dimensional Lattice D4 .

7.3 The Packing Dn

7.4The Dual Lattice Dn*

8. The Lattices E6, E7 and E8

8.1 The 8-Dimensional Lattice E8

8.2 The 7-Dimensional Lattices E7 and E7*

8.3 The 6-Dimensional Lattices E6and E6*

9. The 12-Dimensional Coxeter-Todd Lattice K12

10. The 16-Dimensional Barnes-Wall Lattice A16.

11. The 24-Dimensional Leech Lattice A24

Chapter 5

Sphere Packing and Error-Correcting Codes

J. Leech and N.J.A. Sloane

1. Introduction

1.1 The Coordinate Array of a Point

2. Construction A

2.1 The Construction

2.2 Center Density

2.3 Kissing Numbers

2.4 Dimensions 3 to 6

2.5 Dimensions 7 and 8

2.6 Dimensions 9 to 12

2.7 Comparison of Lattice and Nonlattice Packings

3. Construction B

3.1 The Construction

3.2 Center Density and Kissing Numbers

3.3 Dimensions 8, 9 and 12

3.4 Dimensions 15 to 24

4. Packings Built Up by Layers

4.1 Packing by Layers

4.2 Dimensions 4 to 7

4.3 Dimensions II and 13 to 15

4.4 Density Doubling and the Leech Lattice A,,

4.5 Cross Sections of A24,

5. Other Constructions from Codes

5.1 A Code of Length 40

5.2 A Lattice Packing in R40

5.3 Cross Sections of A40

5.4 Packings Based on Ternary Codes

5.5 Packings Obtained from the Pless Codes

5.6 Packings Obtained from Quadratic Residue Codes

5.7 Density Doubling in R24 and R48

6. Construction C

6.1 The Construction

6.2 Distance Between Centers

6.3 Center Density

6.4 Kissing Numbers

6.5 Packings Obtained from Reed-Muller Codes

6.6 Packings Obtained from BCH and Other Codes

6.7 Density of BCH Packings

6.8 Packings Obtained from Justesen Codes

Chapter 6

Laminated Lattices

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

1. Introduction

2. The Main Results

3. Properties of A0 to A8

4. Dimensions 9 to 16

5. The Deep Holes in A16

6. Dimensions 17 to 24

7. Dimensions 25 to 48

Appendix: The Best Integral Lattices Known

Chapter 7

Further Connections Between Codes and Lattices

N.J.A. Sloane

1. Introduction

2. Construction A

3. Self-Dual (or Type I) Codes and Lattices

4. Extremal Type I Codes and Lattices

5. Construction B

6. Type Ⅱ Codes and Lattices

7. Extremal Type Ⅱ Codes and Lattices

8. Constructions A and B for Complex Lattices

9. Self-Dual Nonbinary Codes and Complex Lattices

10. Extremal Nonbinary Codes and Complex Lattices

Chapter 8

Algebraic Constructions for Lattices

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

1. Introduction

2. The Icosians and the Leech Lattice

……

Chapter 9

Bounds for Codes and Sphere Packings

N.J.A. Sloane

Chapter 10

Three Lectures on Exceptional Groups

J.H. Conway

Chapter 11

The Golay Codes and the Mathieu Groups

J.H. Conway

Chapter 12

A Characterization of the Leech Lattice

J.H. Conway

Chapter 13

Bounds on Kissing Numbers

A.M. Odlyzko and N.J.A. Sloane

Chapter 14

Uniqueness of Certain Spherical Codes

E. Bannai and N.J.A. Sloane

Chapter 15

On the Classification of Integral Quadratic Forms

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

Chapter 16

Enumeration of Unimodular Lattices

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

Chapter 17

The 24-Dimensional Odd Unimodular Lattices

R.E. Borcherds

Chapter 18

Even Unimodular 24-Dimensional Lattices

B.B. Venkov

Chapter 19

Enumeration of Extremal Self-Dual Lattices

J.H. Conway, A.M. Odlyzko and N.J.A. Sloane

Chapter 20

Finding the Closest Lattice Point

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

Chapter 21

Voronoi Cells of Lattices and Quantization Errors

J.H. Conway and N.J.A. SIoane

Chapter 22

A Bound for the Covering Radius of the Leech Lattice

S.P. Norton

Chapter 23

The Covering Radius of the Leech Lattice

J.H. Conway, R.A. Parker and N.J.A. Sloane

Chapter 24

Twenty-Three Constructions for the Leech Lattice

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

Chapter 25

The Cellular Structure of the Leech Lattice

R.E. Borcherds, J.H. Conway and L. Queen

Chapter 26

Lorentzian Forms for the Leech Lattice

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

Chapter 27

The Automorphism Group of the 26-Dimensional Even

Unimodular Lorentzian Lattice

J.H. Conway

Chapter 28

Leech Roots and Vinberg Groups

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

Chapter 29

The Monster Group and its 196884-Dimensional Space

J.H. Conway

Chapter 30

A Monster Lie Algebra?

R.E. Borcherds, J.H. Conway, L. Queen and

N.J.A. Sloane

Bibliography

Supplementary Bibliography

Index