Polyphase Equiangular Tight Frames and Abelian Generalized Quadrangles

Document Type


Publication Date



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.


The "Link to Full Text" button on this page loads the open access e-print at arXiv:1604.07488 [math.FA].
Date of arXiv submission: 26 Apr 2016, updated 1 Jul 2017.

Reviewed at MR3994989.

The publisher's digital version of record for this article is at ScienceDirect as a subscription article. The citation to the final article is noted below.



Source Publication

Applied and Computational Harmonic Analysis