Abstract
An equichordal tight fusion frame (▪) is a finite sequence of equi-dimensional subspaces of a Euclidean space that achieves equality in Conway, Hardin and Sloane's simplex bound. Every ▪ is a type of optimal Grassmannian code, being a way to arrange a given number of members of a Grassmannian so that the minimal chordal distance between any pair of them is as large as possible. Any nontrivial ▪ has both a Naimark complement and spatial complement which themselves are ▪s. We show that taking iterated alternating Naimark and spatial complements of any ▪ of at least five subspaces yields an infinite family of ▪s with pairwise distinct parameters. Generalizing a method by King, we then construct ▪s from difference families for finite abelian groups, and use our Naimark-spatial theory to gauge their novelty.
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