Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets

Authors:
Kanat Abdukhalikov;Eiichi Bannai;Sho Suda
Affiliations:
Institute of Mathematics, Pushkin street 125, Almaty 050010, Kazakhstan;Graduate School of Mathematics, Kyushu University, Hakozaki 6-10-1, Higashi-ku, Fukuoka 812-8581, Japan;Graduate School of Information Sciences, Tohoku University, Aoba, Sendai 680-8570, Japan
Venue:
Journal of Combinatorial Theory Series A
Year:
2009

Citing 5
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Abstract

H. Cohn et al. proposed an association scheme of 64 points in R^1^4 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 collections of real mutually unbiased bases. These schemes are 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.