1.1k citations · 3.7k across the 98 of their papers we have counts for
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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…
On Kissing Numbers in Dimensions 32 to 128
Yves Edel, E. M. Rains, N. J. A. Sloane
An elementary construction using binary codes gives new record kissing numbers in dimensions from 32 to 128.
A Simple Construction for the Barnes-Wall Lattices
G. Nebe, E. M. Rains, N. J. A. Sloane
A certain family of orthogonal groups (called "Clifford groups" by G. E. Wall) has arisen in a variety of different contexts in recent years. These groups have a simple definition…
On the Existence of Similar Sublattices
J. H. Conway, E. M. Rains, N. J. A. Sloane
Partial answers are given to two questions. When does a lattice Lambda contain a sublattice Lambda' of index N that is geometrically similar to Lambda? When is the sublattice "clea…
On Cayley's Enumeration of Alkanes (or 4-Valent Trees)
E. M. Rains, N. J. A. Sloane
Cayley's 1875 enumerations of centered and bicentered alkanes (unlabeled trees of valency at most 4) are corrected and extended -- possibly for the first time in 124 years.