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Unitary and Modular Fourier Transforms of the Symmetric Group over Finite Fields
We give explicit constructions of Fourier transforms for cyclic and symmetric groups over finite fields of characteristic $p$. For a cyclic group of order $N$ in the modular case $p \mid N$, we factor $x^N-1$ and use Bézout's identity to construct a Fourier transform and its inverse. For the symmetr
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