球垛，格点和群：第3版

PrefacetoFirstEdition

PrefacetoThirdEdition

ListofSymbols

Chapter1SpherePackingsandKissingNumbers

Chapter2Coverings,LatticesandQuantizers

Chapter3Codes,DesignsandGroups

Chapter4CertainImportantLatticesandTheirProperties

Chapter5SpherePackingandError-CorrectingCodes

Chapter6LaminatedLattices

Chapter7FurtherConnectionsBetwwenCodesandLattices

Chapter8AlgebraicConstructionsforLattices

Chapter9BoundsforCodesandSpherePackings

Chapter10ThreeLecturesonExceptionalGroups

Chapter11TheGolayCodesandtheMathieuGroups

Chapter12ACharacterizationoftheLeechLattice

Chapter13BoundsonKissingNumbers

Chapter14UniquenessofCertainSphericalCodes

Chapter15OntheClassificationofIntegralQuadraticForms

Chapter16EnumerationofUnimodularLattices

Chapter17The24-DimensionalOddUnimodularLattices

Chapter18EvenUnimodular24-DimensionalLattices

Chapter19EnumerationofExtremalSelf-DualLattices

Chapter20FindingtheClosestLatticePoint

Chapter21VoronoiCellsofLatticesandQuantizationErrors

Chapter22ABoundfortheCoveringRadiusoftheLeechLattice

Chapter23TheCoveringRadiusoftheLeechLattice

Chapter24Twenty-ThreeConstructionsfortheLeechLattice

Chapter25TheCellularStructureoftheLeechLattice

Chapter26LorentzianFormsfortheLeechLattice

Chapter27TheAutomorphismGroupofthe26-DimensionalEvenUnimodularLorentzianLattice

Chapter28LeechRootsandVinbergGroups

Chapter29TheMonsterGroupandits196884-DimensionalSpace

Chapter30AMonsterLieAlgebra?

Bibliography

SupplementaryBibliography

Index

　　本书为第三版，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，本书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。本书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。