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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
Bent Vectorial Functions, Codes and Designs
Bent functions, or equivalently, Hadamard difference sets in the elementary
Abelian group (\gf(2^{2m}), +), have been employed to construct symmetric and
quasi-symmetric designs having the symmetric difference property. The main
objective of this paper is to use bent vectorial functions for a construction
of a two-parameter family of binary linear codes that do not satisfy the
conditions of the Assmus-Mattson theorem, but nevertheless hold -designs. A
new coding-theoretic characterization of bent vectorial functions is presented
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