Frame theory for binary vector spaces

2009/06/18 by Bernhard G. Bodmann, Le Thi My Hanh, Bodmann, Bernhard G. +8 · 1 citation
Computer Science · Mathematics · #12E20 #15A03 #Digital Filter Design and Implementation #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.FA #msc:12E20 #msc:15A03

paper · pdf · doi:10.48550/arxiv.0906.3467

14 pages, LaTeX with AMS macros

arxiv created 2009/06/18 · openalex publication_date 2009/06/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the theory of frames and Parseval frames for finite-dimensional vector spaces over the binary numbers. This includes characterizations which are similar to frames and Parseval frames for real or complex Hilbert spaces, and the discussion of conceptual differences caused by the lack of a proper inner product on binary vector spaces. We also define switching equivalence for binary frames, and list all equivalence classes of binary Parseval frames in lowest dimensions, excluding cases of trivial redundancy.

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• On the Structure of Frames and Equiangular Lines over Finite Fields and their Connections to Design Theory

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