Harmonic Analysis on a Galois Field and Its Subfields
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Complex functions χ(m) where m belongs to a Galois field GF(pℓ), are considered. Fourier transforms, displacements in the GF(pℓ)×GF(pℓ) phase space and symplectic transforms of these functions are studied. It is shown that the formalism inherits many features from the theory of Galois fields. For example, Frobenius transformations and Galois groups are introduced in the present context. The relationship between harmonic analysis on GF(pℓ) and harmonic analysis on its subfields, is studied.
KeywordsPhase space methods Heisenberg-Weyl group Galois fields
Mathematics Subject Classification (2000)81S30 42C30 13B05 12F10
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