Date of Award

3-2025

Document Type

Thesis

Degree Name

Master of Science in Applied Mathematics

Department

Department of Mathematics and Statistics

First Advisor

Matthew Fickus, PhD

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 an optimal Grassmannian code with respect to the chordal distance. We introduce a method for constructing an ECTFF from any finite sequence of unit norm tight frames that happen to be stratified in a certain sense. We moreover show how to construct stratified unit norm tight frames from a difference family for a finite abelian group, as well as from a suitable combination of a resolvable balanced incomplete block design and an equiangular tight frame. These results streamline and unify several known constructions that were previously regarded as disparate, and moreover yield infinitely many apparently new ECTFFs.

AFIT Designator

AFIT-ENC-MS-25-M-240

DTIC Accession Number

AD1356299 ; AD1356619

Comments

An embargo was observed for posting this work on AFIT Scholar.  Approved for public release, Distribution Unlimited. PA Case number 88ABW-2025-0184.

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