Harmonic analysis on a galois field and its subfields
A. Vourdas
Abstract
Complex functions χ(m) where m belongs to a Galois field GF(p ), are considered. Fourier transforms, displacements in the GF(p ) × GF(p ) phase space and symplectic Sp(2,GF(p )) 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 are defined which leave fixed all functions h(n) where n belongs to a subfield GF(p d) of the GF(p ). The relationship between harmonic analysis (or quantum mechanics) on GF(p ) and harmonic analysis on its subfields, is studied.
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