Calculation of Fourier transforms on finite Abelian groups (Corresp.)
G. G. Apple, Paul A. Wintz · IEEE Transactions on Information Theory · 1970
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 onlyN \log_2 Nadditive operations whereNis the order of the group.