Codes and Expansions (CodEx) Seminar

Enrique Gomez-Leos (Iowa State University):
A new infinite family of equiisoclinic tight fusion frames

Equiisoclinic tight fusion frames (EITFFs) generalize the notion of equiangular tight frames (ETFs) to higher-dimensional subspaces. As with ETFs, very few examples of EITFFs are known to exist. In this talk, we demonstrate a method for producing infinitely many new EITFFs. Our constructions all have the feature that the subspace dimension is half the dimension of the ambient space. We completely resolve the existence of such EITFFs in both the real and complex settings. The answer turns out to be closely related to the classical Hurwitz-Radon equations. Furthermore, all such EITFFs feature a remarkable amount of symmetry, and in fact, any even permutation of the subspaces can be realized by a unitary transformation.