Abstract
Finite field Fourier transforms are of great interest in coding and cryptography. They are, in particular, used for describing BCH and RS codes in the spectral domain and for representing the solutions of recurrence equations used in stream ciphers. So far, finite field Fourier transforms have only been defined on vectors that have a length which is relatively prime to the characteristic of the field. The aim of the paper is to generalize this definition to arbitrary lengths. Many properties get a simpler interpretation with this approach.
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