N. J. A. Sloane: Papers on Sphere Packings, Lattices and Quadratic Forms (see also Spherical Codes and Designs)

• New Sphere Packings in Dimensions 9-15, J. Leech and N. J. A. Sloane, Bull. Amer. Math. Soc., 76 (1970), pp. 1006-1010.

• New Sphere Packings in More Than Thirty-Two Dimensions, J. Leech and N. J. A. Sloane, Proceedings Second Chapel Hill Conference on Combinatorial Mathematics and its Applications, Univ. of North Carolina, Chapel Hill, NC, 1970, pp. 345-355.

• Sphere Packing and Error-Correcting Codes, J. Leech and N. J. A. Sloane, Canad. J. Math., 23 (1971), pp. 718-745, A revised version appears as Chapter 5 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.

• Sphere Packings Constructed from BCH and Justesen Codes, N. J. A. Sloane, Mathematika, 19 (1972), pp. 183-190.

• Upper Bounds for Modular Forms, Lattices, and Codes, C. L. Mallows, A. M. Odlyzko and N. J. A. Sloane, J. Algebra, 36 (1975), pp. 68-76.

• Codes over GF(4) and Complex Lattices, N. J. A. Sloane, J. Algebra, 52 (1978), pp. 168-181.

• Binary Codes, Lattices, and Sphere-Packings, N. J. A. Sloane, Combinatorial Surveys: Proceedings of the Sixth British Combinatorial Conference, P. J. Cameron (editor), Academic Press, NY, 1977, pp. 117-164, Russian translation in ``Mathematics: New in Foreign Science'', Vol. 19 (1980), pp. 219-249.

• Extremal Self-Dual Lattices Exist Only in Dimensions 1-8, 12, 14, 15, 23 and 24, J. H. Conway, A. M. Odlyzko and N. J. A. Sloane, Mathematika, 25 (1978), pp. 36-43, A revised version appears as Chapter 19 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.

• Self-Dual Codes and Lattices, N. J. A. Sloane, Relations Between Combinatorics and Other Parts of Mathematics., Proc. Symp. Pure Math., Vol. 34, American Mathematical Society, Providence, RI, 1979, pp. 273-308.

• Tables of Sphere Packings and Spherical Codes, N. J. A. Sloane, IEEE Trans. Information Theory, IT-27 (1981), pp. 327-338.

• On Exceptions of Integral Quadratic Forms, A. M. Odlyzko and N. J. A. Sloane, J. Reine Angew. Math., 321 (1981), pp. 212-216.

• On the Enumeration of Lattices of Determinant One, J. H. Conway and N. J. A. Sloane, J. Number Theory, 15 (1982), pp. 83-94.

• Voronoi Regions of Lattices, Second Moments of Polytopes, and Quantization, J. H. Conway and N. J. A. Sloane, IEEE Trans. Information Theory, IT-28 (1982), pp. 211-226, A revised version appears as Chapter 21 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988. Reprinted in ``Vector Quantization'', H. Abut, Ed., IEEE Press, NY, 1990, pp. 118-133.

• Fast Quantizing and Decoding Algorithms for Lattice Quantizers and Codes, J. H. Conway and N. J. A. Sloane, IEEE Trans. Information Theory, IT-28 (1982), pp. 227-232, Reprinted in ``Vector Quantization'', H. Abut, Ed., IEEE Press, NY, 1990, pp. 134-139.

• Twenty-Three Constructions for the Leech Lattice, J. H. Conway and N. J. A. Sloane, Proc. Roy. Soc. London, Series A, 381 (1982), pp. 275-283, A revised version appears as Chapter 24 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.

• The Covering Radius of the Leech Lattice, J. H. Conway, R. A. Parker and N. J. A. Sloane, Proc. Roy. Soc. London, Series A, 380 (1982), pp. 261-290, A revised version appears as Chapter 23 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.

• Recent Bounds for Sphere Packings and Related Problems Obtained by Linear Programming and Other Methods, N. J. A. Sloane, Papers in Analysis, Algebra and Statistics, Contemporary Math., Vol. 9, R. Lidl (editor), Amer. Math. Soc., Providence, RI, 1982, pp. 153-185, A revised version appears as Chapter 9 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.

• Lorentzian Forms for the Leech Lattice, J. H. Conway and N. J. A. Sloane, Bull. Amer. Math. Soc., 6 (1982), pp. 215-217, A revised version appears as Chapter 26 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.

• On a Problem of Ryskov Concerning Lattice Coverings, R. P. Bambah and N. J. A. Sloane, Acta Arithmetica, 42 (1982), pp. 107-109.

• A Theta-Function Identity for Nonlattice Packings, A. M. Odlyzko and N. J. A. Sloane, Studia Scient. Math. Hungarica, 5 (1980), pp. 461-465.

• Laminated Lattices, J. H. Conway and N. J. A. Sloane, Annals of Math., 116 (1982), pp. 593-620, A revised version appears as Chapter 6 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.

• New Lattice Packings of Spheres, E. S. Barnes and N. J. A. Sloane, Canad. J. Math., 35 (1983), pp. 117-130.

• The Optimal Lattice Quantizer in Three Dimensions, E. S. Barnes and N. J. A. Sloane, SIAM J. Algebraic Discrete Methods, 4 (1983), pp. 30-41.

• The Unimodular Lattices of Dimension up to 23 and the Minkowski-Siegel Mass Constants, J. H. Conway and N. J. A. Sloane, European J. Combinatorics, 3 (1982), pp. 219-231.

• Further Lattice Packings in High Dimensions, A. Bos, J. H. Conway and N. J. A. Sloane, Mathematika, 29 (1982), pp. 171-180.

• A Fast Encoding Method for Lattice Codes and Quantizers, J. H. Conway and N. J. A. Sloane, IEEE Trans. Information Theory, IT-29 (1983), pp. 820-824.

• Complex and Integral Laminated Lattices, J. H. Conway and N. J. A. Sloane, Trans. Amer. Math. Soc., 280 (1983), pp. 463-490.

• The Coxeter-Todd Lattice, The Mitchell Group and Related Sphere Packings, J. H. Conway and N. J. A. Sloane, Math. Proc. Comb. Phil. Soc., 93 (1983), pp. 421-440.

• On the Voronoi Regions of Certain Lattices, J. H. Conway and N. J. A. Sloane, SIAM J. Algebraic Discrete Methods, 5 (1984), pp. 294-305.

• The Packing of Spheres, N. J. A. Sloane, Scientific American, 250 (January, 1984), pp. 116-125, (Also ``Les Empilements de Spheres'', Pour la Science, Mars, 1984, pp. 44-55; ``Kugelpackungen im Raum'', Spektrum der Wissenschaft, March, 1984; ``Empaquetamiento de Esferas'', Investigacion y Ciencia, March 1984, pp. 88-99.).

• On the Classification of Integral Quadratic Forms, J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, NY, Chapter 15, 1988, pp. 352-405.

• A Lower Bound on the Average Error of Vector Quantizers, J. H. Conway and N. J. A. Sloane, IEEE Trans. Information Theory, IT-31 (1985), pp. 106-109.

• Soft Decoding Techniques for Codes and Lattices, Including the Golay Code and the Leech Lattice, J. H. Conway and N. J. A. Sloane, IEEE Trans. Information Theory, IT-32 (1986), pp. 41-50.

• Theta Series and Magic Numbers for Close-Packed Spherical Clusters, N. J. A. Sloane and B. K. Teo, J. Chem. Phys., 83 (1985), pp. 6520-6534.

• New Trellis Codes Based on Lattices and Cosets, A. R. Calderbank and N. J. A. Sloane, IEEE Trans. Information Theory, IT-33 (1987), pp. 177-195.

• Atomic Arrangements and Electronic Requirements for Close-Packed Circular and Spherical Clusters, B. K. Teo and N. J. A. Sloane, Inorganic Chemistry, 25 (1986), pp. 2315-2322.

• An Eight-Dimensional Trellis Code, A. R. Calderbank and N. J. A. Sloane, Proc. IEEE, 74 (1986), pp. 757-759.

• An Improvement to the Minkowski-Hlawka Bound for Packing Superballs, [note: Fig. 1 is in a in separate file] J. A. Rush and N. J. A. Sloane, Mathematika, 34 (1987), pp. 8-18.

• Theta-Series and Magic Numbers for Diamond and Certain Ionic Crystal Structures, [note: Fig. 1 is in a separate file] N. J. A. Sloane, J. Math. Phys., 28 (1987), pp. 1653-1657.

• Penny-Packing and Two-Dimensional Codes, [note: Fig. 1 , Fig. 2 , Fig. 3 , Fig. 4 , Fig. 5 , Fig. 6 are in separate files] R. L. Graham and N. J. A. Sloane, Discrete and Comput. Geom., 5 (1990), pp. 1-11.

• Multi-Dimensional Coding For Error Reduction, A. R. Calderbank and N. J. A. Sloane, U. S. Patent No. 4,581,601, April 8, 1986.

• A Highly Symmetric Four-Dimensional Quasicrystal, V. Elser and N. J. A. Sloane, J. Phys. A., 20 (1987), pp. 6161-6168.

• Low-Dimensional Lattices I: Quadratic Forms of Small Determinant, J. H. Conway and N. J. A. Sloane, Proc. Royal Soc. London, Series A, 418 (1988), pp. 17-41.

• Low-Dimensional Lattices II: Subgroups of GL(n, Z), J. H. Conway and N. J. A. Sloane, Proc. Royal Soc. London, Series A, 419 (1988), pp. 29-68.

• Low-Dimensional Lattices III: Perfect Forms, J. H. Conway and N. J. A. Sloane, Proc. Royal Soc. London, Series A, 418 (1988), pp. 43-80.

• Low-Dimensional Lattices IV: The Mass Formula, J. H. Conway and N. J. A. Sloane, Proc. Royal Soc. London, Series A, 419 (1988), pp. 259-286.

• Low-Dimensional Lattices V: Integral Coordinates for Integral Lattices, J. H. Conway and N. J. A. Sloane, Proc. Royal Soc. London, Series A, 426 (1989), pp. 211-232.

• A New Upper Bound for the Minimum of an Integral Lattice of Determinant One, J. H. Conway and N. J. A. Sloane, Bull. Amer. Math. Soc., 23 (1990), pp. 383-387, Erratum: volume 24 (April 1991), p. 479.

• Multi-Dimensional Coding for Error Reduction, A. R. Calderbank and N. J. A. Sloane, U. S. Patent Re. 33,041, August 29, 1989.

• Lattices with Few Distances, [note: some tables are in a separate file] J. H. Conway and N. J. A. Sloane, J. Number Theory, 39 (1991), pp. 75-90, Also DIMACS Technical Report 90-77, December 1990.

• The Cell Structures of Certain Lattices, [note: Fig. 1a , Fig. 1b , Fig. 2a , Fig. 2b , Fig. 3a , Fig. 3b , Fig. 4 , Fig. 5 , Fig. 6 , Fig. 7 , Fig. 8 , Fig. 9 , Fig. 10 , Fig. 11 , Fig. 12 , Fig. 13 , Fig. 14 , Fig. 15 , Fig. 16a , Fig. 16b , Fig. 17 , Fig. 18 , Fig. 19 , Fig. 20 , Fig. 21 , Fig. 22 , Fig. 23 , Fig. 24 , Fig. 25 , Fig. 26 , are in separate files] J. H. Conway and N. J. A. Sloane, Miscellanea mathematica, P. Hilton, F. Hirzebruch and R. Remmert (editors), Springer-Verlag, NY, 1991, pp. 71-107, Also DIMACS Technical Report 91-5, February 1991.

• On the Covering Multiplicity of Lattices, [note: Fig. 1 , Fig. 2 and Fig. 4 are in separate files] J. H. Conway and N. J. A. Sloane, Discrete and Computational Geometry, 8 (1992), pp. 109-130.

• Trellis Coding Arrangement, A. R. Calderbank and N. J. A. Sloane, U. S. Patent No. 4,939,555, July 3, 1990.

• Low-Dimensional Lattices VI: Voronoi Reduction of Three-Dimensional Lattices, J. H. Conway and N. J. A. Sloane, Proc. Royal Soc. London, Series A, 436 (1992), pp. 55-68.

• Four-Dimensional Lattices With the Same Theta Series, J. H. Conway and N. J. A. Sloane, Duke Math. J., 66 (International Mathematics Research Notices Number 4) (1992), pp. 93-96.

• Sphere Packings, Lattices and Groups (Second Edition), J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1993, 679 pp.

• On Lattices Equivalent to Their Duals, J. H. Conway and N. J. A. Sloane, J. Number Theory, 48 (1994), pp. 373-382, Also DIMACS Technical Report 93-88, December 1993.

• D4, E8, Leech and Certain Other Lattices are Symplectic, J. H. Conway and N. J. A. Sloane, Appendix to P. Buser and P. Sarnak, "On the Period Matrix of a Riemann Surface of Large Genus", Inventiones Math., vol. 117 (1994), pp. 27-56. Also DIMACS Technical Report 93-55, August 1993.

• A Lattice Without a Basis of Minimal Vectors, J. H. Conway and N. J. A. Sloane, Mathematika, 42 (1995), pp. 175-177.

• Minimal-Energy Clusters of Hard Spheres, [note: Fig. 11 , Fig. 12 and "photos" of the putatively optimal clusters of 4 to 10 and 13 to 20 spheres are in separate files] N. J. A. Sloane, R. H. Hardin, T. S. Duff and J. H. Conway, Discrete Computational Geom., 14 (1995), pp. 237-259.

• What Are All the Best Sphere Packings in Low Dimensions?, J. H. Conway and N. J. A. Sloane, Discrete and Computational Geometry (Laszlo Fejes Toth Festschrift), 13 (1995), pp. 383-403.

• The Antipode Construction for Sphere Packings, J. H. Conway and N. J. A. Sloane, Inventiones mathematica, 123 (1996), pp. 309-313.

• On Sublattices of the Hexagonal Lattice, M. Bernstein, N. J. A. Sloane and P. E. Wright, Discrete Math., 170 (1997), pp. 29-39.

• Double Circulant Codes over Z4 and Even Unimodular Lattices, A. R. Calderbank and N. J. A. Sloane, J. Algebraic Combinatorics, 6 (1997), pp. 119-131.

• The Ternary Golay Code, the Integers Mod 9 and the Coxeter-Todd Lattice, A. R. Calderbank and N. J. A. Sloane, IEEE Trans. Inform. Theory, 42 (1996), pp. 636-637. (Unfortunately this paper is wrong: the lattice is not K_12)

• Some Lattices Obtained from Riemann Surfaces , M. Bernstein and N. J. A. Sloane, Extremal Riemann Surfaces (Contemporary Math. Vol. 201), J. R. Quine and P. Sarnak (editors), Amer. Math. Soc., Providence, RI, 1997, pp. 29-32.

• Low-Dimensional Lattices VII: Coordination Sequences [postscript, pdf], J. H. Conway and N. J. A. Sloane, Proc. Royal Soc. London, Series A, 453 (1997), pp. 2369-2389.
• Kugelpackungen im Raum, N. J. A. Sloane, Moderne Mathematik, G. Faltings (editor), Spektrum Akademischer Verlag, Heidelberg, Germany, 1996, pp. 112-123.

• Packing Lines, Planes, etc.: Packings in Grassmannian Space [postscript, pdf], J. H. Conway, R. H. Hardin and N. J. A. Sloane, Experimental Math., 5 (1996), pp. 139-159.
• A Family of Optimal Packings in Grassmannian Manifolds [postscript, pdf], P. W. Shor and N. J. A. Sloane, J. Algebraic Combinatorics, 7 (1998), pp. 157-163.
• A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces [postscript, pdf], A. R. Calderbank, R. H. Hardin, E. M. Rains, P. W. Shor and N. J. A. Sloane, J. Algebraic Combinatorics, 9 (1999), pp. 129-140.
• The Shadow Theory of Modular and Unimodular Lattices, E. M. Rains and N. J. A. Sloane, J. Number Theory, 73 (1998), pp. 359-389.
• A Note on Optimal Unimodular Lattices [postscript, pdf], J. H. Conway and N. J. A. Sloane, J. Number Theory, 72 (1998), pp. 357-362.
• Database of Lattices G. Nebe and N. J. A. Sloane, Published electronically at http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/.

• Packing Planes in Four Dimensions and Other Mysteries [postscript, pdf], N. J. A. Sloane, Algebraic Combinatorics and Related Topics (Yamagata 1997), E. Bannai, M. Harada and M. Ozeki (editors), Yamagata University, Faculty of Science, Department of Mathematics, 1998, 1999.
• On Kissing Numbers in Dimensions 32 to 128 [postscript, pdf], Y. Edel, E. M. Rains and N. J. A. Sloane, Elect. J. Combinatorics 5(1), paper R22 (1998).

• The Sphere Packing Problem [postscript, pdf], N. J. A. Sloane, Proceedings Internat. Congress Math. Berlin 1998, Documenta Mathematika, III (1998), pp. 387-396.
• Kepler's Conjecture Confirmed [postscript, pdf], N. J. A. Sloane, Nature, 395 (October 1, 1998), pp. 435-436.
• On the Existence of Similar Sublattices [postscript, pdf], J. H. Conway, E. M. Rains and N. J. A. Sloane, Canad. J. Math., 1999 submitted.