Totally symmetric Grassmannian codes
Combinatorics
2026-01-23 v2 Information Theory
Functional Analysis
Group Theory
math.IT
Abstract
We introduce a general technique to construct tight fusion frames with prescribed symmetries. Applying this technique with a prescription for "all the symmetries", we construct a new family of equi-isoclinic tight fusion frames (EITFFs), which consequently form optimal Grassmannian codes. By virtue of their construction, our EITFFs have the remarkable property of total symmetry: any permutation of subspaces can be achieved by an appropriate unitary.
Cite
@article{arxiv.2406.19542,
title = {Totally symmetric Grassmannian codes},
author = {Matthew Fickus and Joseph W. Iverson and John Jasper and Dustin G. Mixon},
journal= {arXiv preprint arXiv:2406.19542},
year = {2026}
}
Comments
An early version of this paper appeared on the arXiv with the title "Equi-isoclinic subspaces from symmetry". To help distinguish between the two (very different) versions, the authors also changed the title