A family of group character codes

In IEEE Trans. Inform. Theory 46 (2000), 280, using characters of an elementary Abelian 2-group, a class of q-ary codes, where q is an odd prime power, is constructed. These codes share several features in common with binary Reed–Muller codes. This construction is generalized in this paper to yield codes with features that resemble those of generalized Reed–Muller codes.