Naimark-spatial families of equichordal tight fusion frames
Document Type
Article
Publication Date
11-11-2024
Abstract
An equichordal tight fusion frame (ECTFF) is a finite sequence of equi-dimensional subspaces of a Euclidean space that achieves equality in Conway, Hardin and Sloane's simplex bound. Every ECTFF is a type of optimal Grassmannian code, being a way to arrange a given number of members of a Grassmannian so that the minimal chordal distance between any pair of them is as large as possible. Any nontrivial ECTFF has both a Naimark complement and spatial complement which themselves are ECTFFs. We show that taking iterated alternating Naimark and spatial complements of any ECTFF of at least five subspaces yields an infinite family of ECTFFs with pairwise distinct parameters. Generalizing a method by King, we then construct ECTFFs from difference families for finite abelian groups, and use our Naimark-spatial theory to gauge their novelty.
Source Publication
Applied and Computational Harmonic Analysis ( ISSN 1063-5203 | e-ISSN 1096-603X)
Recommended Citation
Fickus, M., Mayo, B. R., & Watson, C. E. (2025). Naimark-spatial families of equichordal tight fusion frames. Applied and Computational Harmonic Analysis, 74, 101720. https://doi.org/10.1016/j.acha.2024.101720
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The article was published online at ScienceDirect ahead of the issue. It appears in the January 2025 issue of Applied and Computational Harmonic Analysis (volume 74).