Radon-Hurwitz Grassmannian Codes

Every equi-isoclinic tight fusion frame (EITFF) is a type of optimal code ina Grassmannian, consisting of subspaces of a finite-dimensional Hilbert spacefor which the smallest principal angle between any pair of them is as large aspossible. EITFFs yield dictionaries with minimal block coherence and so areideal for certain types of compressed sensing. By refining classical argumentsof Lemmens and Seidel that rely upon Radon-Hurwitz theory, we fullycharacterize EITFFs in the special case where the dimension of the subspaces isexactly one-half of that of the ambient space. We moreover show that each such"Radon-Hurwitz EITFF" is highly symmetric.