- The Cell Structures of Certain Lattices* J. H. Conway
- A Highly Symmetric Four-Dimensional Quasicrystal* Veit Elser and N. J. A. Sloane
- Doublyeven Doublyeven
- Multiple Description Vector Quantization with Lattice Codebooks: Design and Analysis
- On Asymmetric Coverings and Covering Numbers David Applegate, E. M. Rains 1 and N. J. A. Sloane
- A New Approach to the Construction of Optimal Designs* R. H. Hardin
- A New Upper Bound for the Minimum of an Integral Lattice of Determinant One*
- Soft Decoding Techniques for Codes and Lattices, Including the Golay Code and the Leech Lattice *
- D 4 : X = 1 6 : X = \Gamma
- Some Canonical Sequences of Integers \Lambda M. Bernstein and N. J. A. Sloane
- Quaternary Constructions for the Binary Single-Error-Correcting Codes of Julin, Best and Others
- Quantizing Using Lattice Intersections N. J. A. Sloane
- [1] A. Bonnecaze, A. R. Calderbank and P. Sol'e, Quaternary quadratic residue codes and unimodular lattices, IEEE Trans. Inform. Theory, 41 (1995), 366--377 and 1536.
- The EKG Sequence J. C. Lagarias, E. M. Rains and N. J. A. Sloane
- Codes from Symmetry Groups, and a [32, 17, 8] Code* Ying Cheng**
- A New Upper Bound for the Minimum of an Integral Lattice of Determinant One*
- McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions
- Inorg. Chem. 1985, 24, 4545-4558 4545 Contribution from AT&T Bell Laboratories,
- Asymmetric Multiple Description Lattice Vector Suhas N. Diggavi \Lambda , N. J. A. Sloane, and Vinay A. Vaishampayan
- A New Operation on Sequences: The Boustrophedon J. Millar, N. J. A. Sloane and N. E. Young
- Low-Dimensional Lattices IV: The Mass Formula
- The Antipode Construction for Sphere Packings J. H. Conway
- The Solution to Berlekamp's Switching Game* P. C. Fishburn and N. J. A. Sloane
- A STRENGTHENING OF THE ASSMUS-MATTSON THEOREM* A. R. Calderbank
- Interleaver design for Turbo codes H. R. Sadjadpour, N. J. A. Sloane, and G. Nebe, M. Salehi
- A Linear Construction for Certain Kerdock and Preparata Codes*
- A Linear Construction for Certain Kerdock and Preparata Codes*
- A GroupTheoretic Framework for the Construction of Packings in Grassmannian Spaces
- McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions
- On the Apparent Duality of the Kerdock and Preparata Codes ?
- Doc. Math. J. DMV 1 The Sphere Packing Problem
- The Binary Self-Dual Codes of Length Up To 32: A Revised Enumeration* J. H. Conway
- A Family of Optimal Packings in Grassmannian Manifolds P. W. Shor and N. J. A. Sloane
- The Antipode Construction for Sphere Packings J. H. Conway
- SelfDual Codes over the Integers Modulo 4* J. H. Conway
- The Automorphism Group of an [18, 9, 8] Quaternary Code * Ying Cheng**
- The Nordstrom-Robinson Code is the Binary Image of the Octacode
- Lattices with Few Distances* J. H. Conway
- pp + pp 012 pp + pp 023
- The Cell Structures of Certain Lattices * J. H. Conway
- LowDimensional Lattices V: Integral Coordinates for Integral Lattices*
- The NordstromRobinson Code is the Binary Image of the Octacode #
- Unsolved Problems in Graph Theory Arising from the Study of Codes* N. J. A. Sloane
- Interleaver Design for Turbo Codes H. R. Sadjadpour, N. J. A. Sloane, M. Salehi, and G. Nebe
- The Shadow Theory of Modular and Unimodular Lattices E. M. Rains and N. J. A. Sloane
- [14] B. W. Jones, The Arithmetic Theory of Quadratic Forms, Math. Assoc. America, 1950. [15] R. A. Rankin, A minimum problem for the Epstein zetafunction, Proc. Glasgow Math.
- Four Icosahedra Can Meet at a Point* Henri Rossat
- SIAM J. ALG. DISC. METH. Vol. 1, No. 4, December 1980
- The Optimal Lattice Quantizer in Three Dimensions1 E. S. Barnes
- Cyclic Self-Dual Codes1 N. J. A. Sloane
- A Monster Lie Algebra? R. E. Borcherds, J. H. Conway, L. Queen and N. J. A. Sloane
- R. L. Graham and N. J. A. Sloane Mathemutics and Statistics Research Center
- Soft Decoding Techniques for Codes and Lattices, Including the Golay Code and the Leech Lattice*
- Lexicographic Codes: Error-Correcting Codes from Game Theory* J. H. Conway
- An improvement to the Minkowski-Hlawka bound for packing superballs*
- The Automorphism Group of an [18, 9, 8] Quaternary Code* Ying Cheng**
- A [45, 13] Code with Minimal Distance 16* J. H. Conway
- Low-Dimensional Lattices V: Integral Coordinates for Integral Lattices*
- A New Upper Bound on the Minimal Distance of Self-Dual Codes* J. H. Conway
- Unsolved Problems in Graph Theory Arising from the Study of Codes* N. J. A. Sloane
- Low-Dimensional Lattices VI: Voronoi Reduction of Three-Dimensional J. H. Conway
- Computer-Generated Minimal (and Larger) Response-Surface Designs: (I) The Sphere
- Computer-Generated Minimal (and Larger) Response-Surface Designs: (II) The Cube
- Codes (Spherical) and Designs (Experimental) R. H. Hardin and N. J. A. Sloane
- Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites
- Multiple Description Vector Quantization with Lattice Codebooks: Design and Analysis
- A Zador-Like Formula for Quantizers Based on Periodic Tilings N. J. A. Sloane and Vinay A. Vaishampayan
- Clifford-Weil groups of quotient representations. Annika Gunther and Gabriele Nebe
- Unsolved Problems Related to the Covering Radius of Codes* N. J. A. Sloane
- LowDimensional Lattices I: Quadratic Forms of Small Determinant
- The Optimal Lattice Quantizer in Three Dimensions 1 E. S. Barnes
- Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites
- The Number of Hierarchical Orderings N. J. A. Sloane
- [1] J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Second edition, SpringerVerlag, New York, 1993.
- ComputerGenerated Minimal (and Larger) ResponseSurface Designs: (I) The Sphere
- Unsolved Problems Related to the Covering Radius of Codes * N. J. A. Sloane
- New Trellis Codes Based on Lattices and Cosets * A. R. Calderbank and N. J. A. Sloane
- The Solution to Berlekamp's Switching Game * P. C. Fishburn and N. J. A. Sloane
- Low-Dimensional Lattices I: Quadratic Forms of Small Determinant
- [13] M. Klemm, Selbstduale Codes uber dem Ring der ganzen Zahlen modulo 4, Archiv Math.,
- ComputerGenerated Minimal (and Larger) ResponseSurface Designs: (II) The Cube
- Cyclic SelfDual Codes 1 N. J. A. Sloane
- [Map] B. W. Char et al., Maple V language reference manual, SpringerVerlag, NY, 1991. [CoM] H. S. M. Coxeter and W. O. J. Moser, Generators and relations for discrete groups,
- The Number of Hierarchical Orderings N. J. A. Sloane
- The Primary Pretenders John H. Conway, Richard K. Guy, W. A. Schneeberger & N. J. A. Sloane
- Lattices with Few Distances* J. H. Conway
- A ZadorLike Formula for Quantizers Based on Periodic Tilings N. J. A. Sloane and Vinay A. Vaishampayan
- ISIT2000, Sorrento, Italy, June 25--30, 2000 Asymptotic Performance of Multiple Description
- Multiple Description Lattice Vector Quantization \Lambda Sergio D. Servetto y Vinay A. Vaishampayan z N. J. A. Sloane z
- On the Covering Radius of Codes * R. L. Graham
- Interleaver design for short block length Turbo codes H. R. Sadjadpour, M. Salehi, N. J. A. Sloane, and G. Nebe
- Kepler Confirmed N. J. A. Sloane
- Lexicographic Codes: ErrorCorrecting Codes from Game Theory * J. H. Conway
- A Lower Bound on the Average Error of Vector Quantizers
- On the Covering Radius of Codes* R. L. Graham
- Quantum Error Correction and Orthogonal Geometry A. R. Calderbank, 1 E. M. Rains, 2 P. W. Shor, 1 and N. J. A. Sloane 1
- Four Icosahedra Can Meet at a Point * Henri Rossat
- On Kissing Numbers in Dimensions 32 to 128 Mathematisches Institut der Universitat
- Packing Lines, Planes, etc.: Packings in Grassmannian Spaces J. H. Conway
- On the Covering Multiplicity of Lattices* J. H. Conway
- LowDimensional Lattices IV: The Mass Formula
- Anti-Hadamard Matrices* R. L. Graham and N. J. A. Sloane
- LowDimensional Lattices VI: Voronoi Reduction of ThreeDimensional J. H. Conway
- A Nonadditive Quantum Code Eric M. Rains, R. H. Hardin, Peter W. Shor, and N. J. A. Sloane
- [38] M. Yamada, Distanceregular digraphs of girth 4 over an extension ring of Z=4Z, Graphs and Combinatorics, 6 (1990), 381--394.
- A [45, 13] Code with Minimal Distance 16* J. H. Conway
- A Nonadditive Quantum Code Eric M. Rains, R. H. Hardin, Peter W. Shor, and N. J. A. Sloane
- Self-Dual Codes over the Integers Modulo 4* J. H. Conway
- 4-Linearity of Kerdock, Preparata, Goethals and Related Codes A. Roger Hammons, Jr.**
- [1] E. F. Assmus, Jr., and H. F. Mattson, Jr., personal communication. [2] J. H. Conway and N. J. A. Sloane, SpherePackings, Lattices and Groups, SpringerVerlag,
- Mukerjee, R., & Wu, C. F. J. (1995). On the existence of saturated and nearly saturated asymmetrical orthogonal arrays. Ann. Statist. To appear.
- [Ha92] T. C. Hales, The sphere packing problem, J. Computational and Applied Math., 44 (1992), 41--76.
- AntiHadamard Matrices * R. L. Graham and N. J. A. Sloane
- A Lower Bound on the Average Error of Vector Quantizers
- Codes from Symmetry Groups, and a [32, 17, 8] Code* Ying Cheng**
- A Monster Lie Algebra? R. E. Borcherds, J. H. Conway, L. Queen and N. J. A. Sloane
- Design of Asymmetric Multiple Description Lattice Vector Quantizers
- UPDATED TABLES OF PARAMETERS OF (T; M;S)NETS Andrew T. Clayman, K. Mark Lawrence, Gary L. Mullen,
- PennyPacking and TwoDimensional Codes * R. L. Graham and N. J. A. Sloane
- A New Upper Bound on the Minimal Distance of SelfDual Codes* J. H. Conway
- A STRENGTHENING OF THE ASSMUSMATTSON THEOREM* A. R. Calderbank
- Efficient Regression Verification R. H. Hardin*
- A New Operation on Sequences: The Boustrophedon Transform #
- OPERATING MANUAL FOR GOSSET: A GENERAL-PURPOSE PROGRAM FOR CONSTRUCTING
- Quaternary Constructions for the Binary SingleErrorCorrecting Codes of Julin, Best and Others #
- On the Existence of Similar Sublattices J. H. Conway
- OPERATING MANUAL FOR GOSSET: A GENERAL PURPOSE PROGRAM FOR CONSTRUCTING
- 4 M. BERNSTEIN AND N. J. A. SLOANE [C] J.H. Conway and N.J.A. Sloane, On Lattices Equivalent to Their Duals, Journal of Number
- Interleaver design for short block length Turbo codes H. R. Sadjadpour, M. Salehi, N. J. A. Sloane, and G. Nebe
- On the Existence of Similar Sublattices J. H. Conway
- An improvement to the MinkowskiHlawka bound for packing superballs *
- The Z 4 Linearity of Kerdock, Preparata, Goethals and Related Codes # A. Roger Hammons, Jr.**
- A Highly Symmetric FourDimensional Quasicrystal * Veit Elser and N. J. A. Sloane
- The EKG Sequence J. C. Lagarias, E. M. Rains and N. J. A. Sloane
- On the Covering Multiplicity of Lattices* J. H. Conway
- On Asymmetric Coverings and Covering Numbers David Applegate, E. M. Rains1 and N. J. A. Sloane
- Penny-Packing and Two-Dimensional Codes* R. L. Graham and N. J. A. Sloane
- Interleaver Design for Turbo Codes H. R. Sadjadpour, N. J. A. Sloane, M. Salehi, and G. Nebe
- A New Approach to the Construction of Optimal Designs* R. H. Hardin
- The Binary SelfDual Codes of Length Up To 32: A Revised Enumeration* J. H. Conway
- Figure 1: Putatively optimal clusters of N spheres, for N = 4 \Gamma 10 (figures (a)--(g)) and 13--20 (figures (h)--(o)). For greater clarity the spheres have been reduced in size, contacts between
- [15] R. H. Hardin and N. J. A. Sloane, ``A new approach to the construction of optimal designs,'' preprint, 1992.
- The Primary Pretenders John H. Conway, Richard K. Guy, W. A. Schneeberger & N. J. A. Sloane
- Correction to: "The Ternary Golay Code, the Integers Mod 9 and the Coxeter-Todd Lattice," [IEEE Trans. Inform. Theory,
