Document Type

Article

Publication Date

11-25-2019

Abstract

An equiangular tight frame (ETF) is a type of optimal packing of lines in a finite-dimensional Hilbert space. ETFs arise in various applications, such as waveform design for wireless communication, compressed sensing, quantum information theory and algebraic coding theory. In a recent paper, signature matrices of ETFs were constructed from abelian distance regular covers of complete graphs. We extend this work, constructing ETF synthesis operators from abelian generalized quadrangles, and vice versa. This produces a new infinite family of complex ETFs as well as a new proof of the existence of certain generalized quadrangles. This work involves designing matrices whose entries are polynomials over a finite abelian group. As such, it is related to the concept of a polyphase matrix of a finite filter bank.

Comments

Sourced from the e-print (version 2) at arXiv:1604.07488v2 [math.FA]. https://arxiv.org/abs/1604.07488
Date of arXiv submission (version 2): 1 Jul 2017

The publisher's digital version of record for this article is at ScienceDirect: https://doi.org/10.1016/j.acha.2017.11.007

'Date of publication' refers to the publisher version.

DOI

10.1016/j.acha.2017.11.007

Source Publication

Applied and Computational Harmonic Analysis

Share

COinS