In large-characteristic finite fields, equiangular lines form tight frames exactly when they meet the Welch bound and their triple-product sums match a fixed value.
Tight frames over the quaternions and equiangular lines
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We show that much of the theory of finite tight frames can be generalised to vector spaces over the quaternions. This includes the variational characterisation, group frames, and the characterisations of projective and unitary equivalence. We are particularly interested in sets of equiangular lines (equi-isoclinic subspaces) and the groups associated with them, and how to move them between the spaces $\Rd$, $\Cd$ and $\Hd$. We discuss what the analogue of Zauner's conjecture for equiangular lines in $\Hd$ might be.
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On the Structure of Frames and Equiangular Lines over Finite Fields and their Connections to Design Theory
In large-characteristic finite fields, equiangular lines form tight frames exactly when they meet the Welch bound and their triple-product sums match a fixed value.