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Book Information

Author(s): J. H. Conway and N. J. A. Sloane
Title: Sphere packings, lattices and groups
Additional book information: Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, 1988, xxviii + 663 pp., $87.00. ISBN 0-387-96617-X, and ISBN 3-540-96617-X

1.: Eiichi Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canad. J. Math. 33 (1981), 437-449. MR 617634
2.: C. Bender, Bestimmung der grössten Anzahl gleich Kugeln, welche sich auf ein Kugel von demselben Radius, wie die übrigen, auflegen lassen, Arch Math. Phys. (Grunert) 56 (1874), 302-306.
3.: Elwyn R. Berlekamp, John H. Conway and Richard K. Guy, Winning Ways for your Mathematical Plays, Chapter 14, Academic Press, New York, 1982.
4.: A. H. Boerdijk, Some remarks concerning close-packing of equal spheres, Philips Res. Rep. 7(1952), 303-313. MR 50302
5.: R. E. Borcherds, J. H. Conway, L. Queen and N. J. A. Sloane, A monster Lie algebra? Adv. in Math. 53 (1984), 75-79. MR 748897
6.: J. H. Conway, A characterization of Leech's lattice, Invent. Math. 7 (1969), 137-142. MR 245518
7.: J. H. Conway, Three lectures on exceptional groups, Finite Simple Groups (M. B. Powell and G. Higman, eds. ), Academic Press, New York, 1971, pp. 215-247. MR 338152
8.: J. H. Conway, The automorphism group of the 26-dimensional even unimodular Lorentzian lattice, J. Algebra 80 (1983), 159-163. MR 690711
9.: J. H. Conway and S. P. Norton, Monstrous moonshine, Bull. London Math. Soc. 11 (1979), 308-339. MR 554399
10.: J. H. Conway, A. M. Odlyzko and N. J. A. Sloane, Extremal self-dual lattices exist only in dimensions 1 to 8, 12, 14, 15, 23 and 24, Mathematika 25 (1978), 36-43. MR 505767
11.: J. H. Conway, R. A. Parker and N. J. A. Sloane, The covering radius of the Leech lattice, Proc. Roy Soc. London A380 (1982), 261-290. MR 660415
12.: J. H. Conway and N. J. A. Sloane, On the enumeration of lattices of determinant one, J. Number Theory 14 (1982), 83-94. MR 666350
13.: J. H. Conway and N. J. A. Sloane, Voronoi regions of lattices, second moments of polytopes, and quantization, I.E.E.E. Trans. Info. Theory 28 (1982), 211-226. MR 651816
14.: J. H. Conway and N. J. A. Sloane, Twenty-three constructions for the Leech lattice, Proc. Roy. Soc. London A381 (1982), 275-283. MR 661720
15.: J. H. Conway and N. J. A. Sloane, Lorentzian forms for the Leech lattice, Bull. Amer. Math. Soc. (N.S.) 6 (1982), 215-217. MR 640949
16.: J. H. Conway and N. J. A. Sloane, Laminated lattices, Ann. of Math. (2) 116 (1982), 593-620. MR 678483
17.: J. H. Conway and N. J. A. Sloane, Leech roots and Vinberg groups, Proc. Roy. Soc. London A384 (1982), 233-258. MR 684311
18.: J. H. Conway and N. J. A. Sloane, The unimodular lattices of dimension up to 23 and the Minkowski-Siegel mass constants, Europ. J. Combin. 3 (1982), 219-231. MR 679207
19.: J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, I.E.E.E. Trans. Info. Theory 32 (1986), 337-348. MR 838197
20.: J. H. Conway and N. J. A. Sloane, Low-dimensional lattices. III Perfect forms, Proc. Roy. Soc. London Ser. A 418 (1988), no. 1854, 43-80. MR 953277
21.: C. F. Gauss, Besprechung des Buchs von L. A. Seeber: Untersuchungen über die Eigenschaften der positiven ternaren quadratischen Formen usw., Göttingsche gelehrte Anzeigen (1831-07-09)=Werke, II (1876), 188-196.
22.: S. Günther, Ein stereometrisches Problem, Arch. Math. Phys. (Grunert) 57 (1875), 209-215.
23.: R. Hoppe, Bemerkung der Redaktion, Arch. Math. Phys. (Grunert) 56 (1874), 307-312.
24.: J. Leech, The problem of the thirteen spheres, Math. Gaz. 40 (1956), 22-23. MR 76369
25.: J. Leech and N. J. A. Sloane, Sphere packing and error-correcting codes, Canad. J. Math. 23 (1971), 718-745. MR 285994
26.: James G. Propp, Kepler's spheres and Rubik's cube, Math. Mag. 61 (1988), 231-239. MR 962584
27.: S. P. Norton, A bound for the covering radius of the Leech lattice, Proc. Roy. Soc. London A380 (1982), 259-260. MR 660414
28.: A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, J. Combin. Theory Ser. A 26 (1979), 210-214. MR 530296
29.: Arnold Pizer, A note on a conjecture of Hecke, Pacific J. Math. 79 (1978), 541-548; MR 80g: 10028. MR 531334
30.: C. A. Rogers, The packing of equal spheres, Proc. London Math. Soc. 8 (1958), 609-620. MR 102052
31.: N. J. A. Sloane, Recent bounds for codes, sphere packings and related problems obtained by linear programming and other methods, Contemporary Math. vol. 9, Amer. Math. Soc. Providence, R. I., 1982, pp. 153-185. MR 655979
32.: Thomas M. Thompson, From error-correcting codes through sphere packings to simple groups, Carus Math. Monograph 21, Math. Assoc. Amer., Washington DC, 1983. MR 749038
33.: B. B. Venkov, The classification of integral even unimodular 24-dimensional quadratic forms, Trudy Mat. Inst. Steklov 148 (1978), 65-76=Proc. Steklov Inst. Math. no. 4 (1980), 63-74. MR 558941

Review Information:
Journal: Bull. Amer. Math. Soc. 21 (1989), 142-147.
DOI: 10.1090/S0273-0979-1989-15795-9
PII: S 0273-0979(1989)15795-9

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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