A generalized DFT for Abelian codes over Z_m

A generalized discrete Fourier transform defined over an appropriate extension ring is given that is suitable to characterize Abelian codes over residue class integer rings Zm. The characterization is in terms of generalized discrete Fourier transform components taking values from certain ideals of the extension ring. It is shown that the results known for cyclic codes over Zm, like the simple characterization of dual and self-dual codes and the nonexistence of self-dual codes for certain values of code parameters, extend to Abelian codes over Zm as well