Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets
arXiv:0802.1425 · doi:10.1016/j.jcta.2008.07.002
Abstract
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.
16 pages
References in corpus (4)
Cited by in corpus (6)
- Commutative association schemes
- Uniformity in association schemes and coherent configurations: cometric Q-antipodal schemes and linked systems
- Symplectic spreads, planar functions and mutually unbiased bases
- New pseudo-planar binomials in characteristic two and related schemes
- Equivalence classes of Niho bent functions
- Association schemes related to Delsarte-Goethals codes