Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets
Combinatorics
2026-01-27 v1 General Mathematics
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.
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Cite
@article{arxiv.0802.1425,
title = {Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets},
author = {Kanat Abdukhalikov and Eiichi Bannai and Sho Suda},
journal= {arXiv preprint arXiv:0802.1425},
year = {2026}
}
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16 pages