Document Type

Article

Publication Date

6-20-2016

Abstract

An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a few methods for constructing them are known. Motivated by the connection between real ETFs and graph theory, we introduce the notion of ETFs that are symmetric about their centroid. We then discuss how well-known constructions, such as harmonic ETFs and Steiner ETFs, can have centroidal symmetry. Finally, we establish a new equivalence between centroid-symmetric real ETFs and certain types of strongly regular graphs (SRGs). Together, these results give the first proof of the existence of certain SRGs, as well as the disproofs of the existence of others.

Comments

arXiv:1509.04059v2 ; https://arxiv.org/abs/1509.04059.
Date of publication refers to the arXiv e-print, version 2.

Publisher version at ScienceDirect: https://doi.org/10.1016/j.acha.2016.06.004

DOI

10.1016/j.acha.2016.06.004

Source Publication

Applied and Computational Harmonic Analysis

Included in

Mathematics Commons

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