# Codes and Expansions (CodEx) Seminar

## Matthew Fickus (Air Force Institute of Technology)

Harmonic Grassmannian codes

An equi-isoclinic tight fusion frame (EITFF) is a type of Grassmannian code, being a sequence of subspaces of a finite-dimensional Hilbert space of a given dimension with the property that the smallest spectral distance between any pair of them is as large as possible. EITFFs arise in compressed sensing, yielding dictionaries with minimal block coherence. Despite this, they remain poorly understood, with known constructions falling far short of known necessary conditions on their existence. We construct new infinite families of EITFFs in a way that generalizes the known equivalence between harmonic equiangular tight frames and difference sets for finite abelian groups.