The eigenstructure and Jordan form of the Fourier transform over fields of characteristic 2 and a generalized Vandermonde-type formula

DOI10.1016/J.LAA.2015.12.021zbMath1331.12004OpenAlexW2283726756MaRDI QIDQ252622

F. Blanchet-Sadri, M. Dambrine

Publication date: 3 March 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2015.12.021

zbMATH Keywords

eigenstructurefields of characteristic 2finite field Fourier transformsVandermonde's formula

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Eigenvalues, singular values, and eigenvectors (15A18) Finite fields (field-theoretic aspects) (12E20) Other transforms and operators of Fourier type (43A32)

Cites Work

• Fast algorithms for solving Toeplitz systems of equations using number-theoretic transforms
• Cosine transforms over fields of characteristic 2
• Fast, prime factor, discrete Fourier transform algorithms over \(\text{GF}(2^m)\) for \(8 \leqslant m \leqslant 10\)
• Fast Algorithms for Signal Processing
• Closed-Form Orthogonal Number Theoretic Transform Eigenvectors and the Fast Fractional NTT
• Algebraic Codes for Data Transmission

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