2112.14267 ; As published:10.1016/j.acha.2023.01.009">


Harmonic Grassmannian Codes

Document Type


Publication Date



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. Their existence remains poorly characterized. Most known EITFFs have parameters that match those of one that arose from an equiangular tight frame (ETF) in a rudimentary, direct-sum-based way. In this paper, we construct new infinite families of non-"tensor-sized" EITFFs in a way that generalizes the one previously known infinite family of them as well as the celebrated equivalence between harmonic ETFs and difference sets for finite abelian groups. In particular, we construct EITFFs consisting of Q planes in CQ for each prime power Q≥4, of Q−1 planes in CQ for each odd prime power Q, and of 11 three-dimensional subspaces in R11. The key idea is that every harmonic EITFF -- one that is the orbit of a single subspace under the action of a unitary representation of a finite abelian group -- arises from a smaller tight fusion frame with a nicely behaved "Fourier transform." Our particular constructions of harmonic EITFFs exploit the properties of Gauss sums over finite fields.


The "Link to Full Text" on this page opens the arXiv e-print version of the article, hosted at the arXiv repository.

The article's published version of record is available by subscription to the journal, Applied and Computational Harmonic Analysis through the DOI link below.

Current AFIT faculty, students and staff may access the published article from the journal by clicking here.


arXiv:2112.14267 ; As published:10.1016/j.acha.2023.01.009

Source Publication

Applied and Computational Harmonic Analysis