27,917 research outputs found

    Metric dimension of dual polar graphs

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    A resolving set for a graph Γ\Gamma is a collection of vertices SS, chosen so that for each vertex vv, the list of distances from vv to the members of SS uniquely specifies vv. The metric dimension μ(Γ)\mu(\Gamma) is the smallest size of a resolving set for Γ\Gamma. We consider the metric dimension of the dual polar graphs, and show that it is at most the rank over R\mathbb{R} of the incidence matrix of the corresponding polar space. We then compute this rank to give an explicit upper bound on the metric dimension of dual polar graphs.Comment: 8 page

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

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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 page
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