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.

翻译：我们提出了一种通用技术来构建具有指定对称性的紧融合框架。通过应用这项技术并指定"所有对称性"，我们构建了一个新的等距倾斜紧融合框架族，从而形成最优的格拉斯曼码。得益于其构造方式，我们的等距倾斜紧融合框架具备完全对称的卓越特性：任意子空间的置换均可通过适当的酉变换实现。