Dewey Class 
519 
Title 
Sphere Packings, Lattices and Groups ([EBook]) / by J. H. Conway, N. J. A. Sloane. 
Author 
Conway, John Horton 
Added Personal Name 
Sloane, N. J. A.(Neil James Alexander) , 1939 
Other name(s) 
SpringerLink (Online service) 
Edition statement 
Third Edition. 
Publication 
New York, NY : Springer , 1999. 
Physical Details 
LXXIV, 706 pages : online resource. 
Series 
Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 00727830 ; ; 290 
ISBN 
9781475765687 
Summary Note 
We now apply the algorithm above to find the 121 orbits of norm 2 vectors from the (known) nann 0 vectors, and then apply it again to find the 665 orbits of nann 4 vectors from the vectors of nann 0 and 2. The neighbors of a strictly 24 dimensional odd unimodular lattice can be found as follows. If a norm 4 vector v E II . corresponds to the sum 25 1 of a strictly 24 dimensional odd unimodular lattice A and a !dimensional lattice, then there are exactly two nonn0 vectors of ll25,1 having inner product 2 with v, and these nann 0 vectors correspond to the two even neighbors of A. The enumeration of the odd 24dimensional lattices. Figure 17.1 shows the neighborhood graph for the Niemeier lattices, which has a node for each Niemeier lattice. If A and B are neighboring Niemeier lattices, there are three integral lattices containing A n B, namely A, B, and an odd unimodular lattice C (cf. [Kne4]). An edge is drawn between nodes A and B in Fig. 17.1 for each strictly 24dimensional unimodular lattice arising in this way. Thus there is a onetoone correspondence between the strictly 24dimensional odd unimodular lattices and the edges of our neighborhood graph. The 156 lattices are shown in Table 17 .I. Figure I 7. I also shows the corresponding graphs for dimensions 8 and 16.: 
Contents note 
1 Sphere Packings and Kissing Numbers  2 Coverings, Lattices and Quantizers  3 Codes, Designs and Groups  4 Certain Important Lattices and Their Properties  5 Sphere Packing and ErrorCorrecting Codes  6 Laminated Lattices  7 Further Connections Between Codes and Lattices  8 Algebraic Constructions for Lattices  9 Bounds for Codes and Sphere Packings  10 Three Lectures on Exceptional Groups  11 The Golay Codes and the Mathieu Groups  12 A Characterization of the Leech Lattice  13 Bounds on Kissing Numbers  14 Uniqueness of Certain Spherical Codes  15 On the Classification of Integral Quadratic Forms  16 Enumeration of Unimodular Lattices  17 The 24Dimensional Odd Unimodular Lattices  18 Even Unimodular 24Dimensional Lattices  19 Enumeration of Extremal SelfDual Lattices  20 Finding the Closest Lattice Point  21 Voronoi Cells of Lattices and Quantization Errors  22 A Bound for the Covering Radius of the Leech Lattice  23 The Covering Radius of the Leech Lattice  24 TwentyThree Constructions for the Leech Lattice  25 The Cellular Structure of the Leech Lattice  26 Lorentzian Forms for the Leech Lattice  27 The Automorphism Group of the 26Dimensional Even Unimodular Lorentzian Lattice  28 Leech Roots and Vinberg Groups  29 The Monster Group and its 196884Dimensional Space  30 A Monster Lie Algebra?  Supplementary Bibliography. 
System details note 
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Internet Site 
http://dx.doi.org/10.1007/9781475765687 
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