Radon-Hurwitz Grassmannian codes
arxiv(2024)
摘要
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.
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