Totally symmetric Grassmannian codes

TL;DR

This paper introduces a novel construction method for symmetric tight fusion frames, resulting in optimal Grassmannian codes with total symmetry, enhancing the design of highly symmetric subspace arrangements.

Contribution

The paper presents a new technique for constructing totally symmetric equi-isoclinic tight fusion frames, advancing the theory of optimal Grassmannian codes.

Findings

Constructed a new family of totally symmetric EITFFs

Achieved optimal Grassmannian codes with total symmetry

Demonstrated the unitary permutation property of subspaces

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.