A GENERALIZED DFT FOR ABELIAN CODES OVER Z(M)

A generalized discrete Fourier transform defined over an appropriate e xtension ring is given that is suitable to characterize Abelian codes over residue class integer rings Z(m). The characterization is in term s of generalized discrete Fourier transform components taking values f rom certain ideals of the extension ring. It is shown that the results known for cyclic codes over Z(m), 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 Z(m) a s well.