Frame theory for binary vector spaces

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.