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

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Abdukhalikov, Kanat
Bannai, Eiichi
Suda, Sho
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Abstract
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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 pages
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Mathematics - Combinatorics, Mathematics - General Mathematics, 05E30, 94B60, 51M15, 11H06
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