A Note on Totally Symmetric Equi-Isoclinic Tight Fusion Frames

Matthew Fickus, Joseph W. Iverson, John Jasper, Dustin G. Mixon

Abstract: Consider the fundamental problem of arranging r-dimensional subspaces of R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sup> in such a way that maximizes the minimum distance between unit vectors in different subspaces. It is well known that equi-isoclinic tight fusion frames (EITFFs) are optimal for this packing problem, but such ensembles are notoriously hard to construct. In this paper, we present a novel construction of EITFFs that are totally symmetric: any permutation of the subspaces can be realized by an orthogonal transformation of ℝ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sup> .