Polyphase Equiangular Tight Frames and Abelian Generalized Quadrangles

Authors

Matthew C. Fickus, Air Force Institute of TechnologyFollow
John Jasper, University of Cincinnati
Dustin G. Mixon, Air Force Institute of Technology
Jesse D. Peterson, Air Force Institute of Technology
Cody E. Watson, Air Force Institute of Technology

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

Reviewed at MR3994989.

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DOI

10.1016/j.acha.2017.11.007

Source Publication

Applied and Computational Harmonic Analysis (ISSN 1063-5203 | eISSN 1096-603X)

Recommended Citation

Fickus, M. C., Jasper, J., Mixon, D. G., Peterson, J. D., & Watson, C. E. (2019). Polyphase equiangular tight frames and abelian generalized quadrangles. Applied and Computational Harmonic Analysis, 47(3), 628–661. https://doi.org/10.1016/j.acha.2017.11.007