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Calculation of Fourier transforms on finite Abelian groups (Corresp.)

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A recent paper by Crimmins et al. deals with minimization of mean-square error for group codes by the use of Fourier transforms on groups. In this correspondence a method for representing the groups in a form suitable for machine calculation is shown. An efficient method for calculating the Fourier transform of a group is also proposed and its relationship to the fast Fourier transform is shown. For groups of characteristic two, the calculation requires only N \log _2 N additive operations where N is the order of the group.

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Information Theory, IEEE Transactions on  (Volume:16 ,  Issue: 2 )