179 citations · 476 across the 32 of their papers we have counts for
12 papers · 1 filter
Packing Lines, Planes, etc.: Packings in Grassmannian Space
J. H. Conway, R. H. Hardin, N. J. A. Sloane
This paper addresses the question: how should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The results of exten…
A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces
A. R. Calderbank, R. H. Hardin, E. M. Rains +2
By using totally isotropic subspaces in an orthogonal space Omega^{+}(2i,2), several infinite families of packings of 2^k-dimensional subspaces of real 2^i-dimensional space are co…
The Shadow Theory of Modular and Unimodular Lattices
E. M. Rains, N. J. A. Sloane
It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[n/24] +2, unless n = 23 when the bound must be increased by 1. This result was previously known only…
A Note on Optimal Unimodular Lattices
J. H. Conway, N. J. A. Sloane
The highest possible minimal norm of a unimodular lattice is determined in dimensions n <= 33. There are precisely five odd 32-dimensional lattices with the highest possible minima…
McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions
R. H. Hardin, N. J. A. Sloane
Evidence is presented to suggest that, in three dimensions, spherical 6-designs with N points exist for N=24, 26, >= 28; 7-designs for N=24, 30, 32, 34, >= 36; 8-designs for N=36,…
On Single-Deletion-Correcting Codes
N. J. A. Sloane
This paper gives a brief survey of binary single-deletion-correcting codes. The Varshamov-Tenengolts codes appear to be optimal, but many interesting unsolved problems remain. The…