Totally symmetric Grassmannian codes

We introduce a general technique to construct tight fusion frames with prescribed symmetries. Applying this technique with a prescription for "all the symmetries", we construct a new family of equi-isoclinic tight fusion frames (EITFFs), which consequently form optimal Grassmannian codes. By virtue of their construction, our EITFFs have the remarkable property of total symmetry: any permutation of subspaces can be achieved by an appropriate unitary.