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

翻译：每个等角紧密融合框架（EITFF）都是格拉斯曼流形中的一种最优码，由有限维希尔伯特空间的子空间构成，其中任意一对子空间之间的最小主角度尽可能大。EITFF 能生成具有最小块相干性的字典，因此对某些类型的压缩感知问题具有理想特性。通过精炼 Lemmens 和 Seidel 基于 Radon-Hurwitz 理论的经典论证，我们在子空间维度恰好为环境空间维度一半的特殊情形下，完整刻画了 EITFF。此外，我们证明每个这样的 "Radon-Hurwitz EITFF" 都具有高度对称性。