Document Type

Article

Publication Date

7-1-2017

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

arXiv:1604.07488v2 [math.FA] ; http://arxiv.org/abs/1604.0748
Publication date refers to arXiv e-print version 2.

Publisher version at: https://doi.org/10.1016/j.acha.2017.11.007

DOI

10.1016/j.acha.2017.11.007

Source Publication

Applied and Computational Harmonic Analysis

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