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Title: Frames over finite fields: equiangular lines in orthogonal geometry
Authors: Greaves, Gary Royden Watson
Iverson, Joseph W.
Jasper, John
Mixon, Dustin G.
Keywords: Science::Mathematics
Issue Date: 2022
Source: Greaves, G. R. W., Iverson, J. W., Jasper, J. & Mixon, D. G. (2022). Frames over finite fields: equiangular lines in orthogonal geometry. Linear Algebra and Its Applications, 639, 50-80.
Project: RG29/18
Journal: Linear Algebra and Its Applications
Abstract: We investigate equiangular lines in finite orthogonal geometries, focusing specifically on equiangular tight frames (ETFs). In parallel with the known correspondence between real ETFs and strongly regular graphs (SRGs) that satisfy certain parameter constraints, we prove that ETFs in finite orthogonal geometries are closely aligned with a modular generalization of SRGs. The constraints in our finite field setting are weaker, and all but 18 known SRG parameters on v≤1300 vertices satisfy at least one of them. Applying our results to triangular graphs, we deduce that Gerzon's bound is attained in finite orthogonal geometries of infinitely many dimensions. We also demonstrate connections with real ETFs, and derive necessary conditions for ETFs in finite orthogonal geometries. As an application, we show that Gerzon's bound cannot be attained in a finite orthogonal geometry of dimension 5.
ISSN: 0024-3795
DOI: 10.1016/j.laa.2021.11.024
Rights: © 2022 Elsevier Inc. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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