322 research outputs found

    Tremain equiangular tight frames

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    Equiangular tight frames provide optimal packings of lines through the origin. We combine Steiner triple systems with Hadamard matrices to produce a new infinite family of equiangular tight frames. This in turn leads to new constructions of strongly regular graphs and distance-regular antipodal covers of the complete graph.Comment: 11 page

    On Distance-Regular Graphs with Smallest Eigenvalue at Least βˆ’m-m

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    A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer mβ‰₯2m\geq 2, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least βˆ’m-m, diameter at least three and intersection number c2β‰₯2c_2 \geq 2

    Tremain Equiangular Tight Frames

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    Equiangular tight frames provide optimal packings of lines through the origin. We combine Steiner triple systems with Hadamard matrices to produce a new infinite family of equiangular tight frames. This in turn leads to new constructions of strongly regular graphs and distance-regular antipodal covers of the complete graph
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