Codes of the Reed–Muller Type on a Finite Abelian Group

Codes of the Reed–Muller type are introduced with the help of certain sets of complex-valued functions on a finite Abelian group. In the case of an elementary Abelian 2-group, these are ordinary binary Reed–Muller codes. For codes of the Reed–Muller type, some of the algebraic properties well known for standard Reed–Muller codes are proved.