4 research outputs found
Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets
H. Cohn et. al. proposed an association scheme of 64 points in R^{14} which
is conjectured to be a universally optimal code. We show that this scheme has a
generalization in terms of Kerdock codes, as well as in terms of maximal real
mutually unbiased bases. These schemes also related to extremal line-sets in
Euclidean spaces and Barnes-Wall lattices. D. de Caen and E. R. van Dam
constructed two infinite series of formally dual 3-class association schemes.
We explain this formal duality by constructing two dual abelian schemes related
to quaternary linear Kerdock and Preparata codes.Comment: 16 page
Experimental study of energy-minimizing point configurations on spheres
In this paper we report on massive computer experiments aimed at finding
spherical point configurations that minimize potential energy. We present
experimental evidence for two new universal optima (consisting of 40 points in
10 dimensions and 64 points in 14 dimensions), as well as evidence that there
are no others with at most 64 points. We also describe several other new
polytopes, and we present new geometrical descriptions of some of the known
universal optima.Comment: 41 pages, 12 figures, to appear in Experimental Mathematic