Construction of Self-Dual Radical 2-Codes of given Distance

A linear code C is called a group code if C is an ideal in a group algebra K[G] where K is a ring and G is a finite group. Many classical linear error-correcting codes can be realized as ideals of group algebras. Berman [1], in the case of characteristic 2, and Charpin [2], for characteristic p = 2, proved that all generalized Reed–Muller codes coincide with powers of the radical of the group algebra over an elementary abelian p-group. These codes form an important class containing many codes of practical value. Landrock and Manz [5] showed the relation between these results and the classical result of Jennings [4] related to the structure of the radical of group algebra GF (p)[G], where G is a finite p-group. In this paper we solve Problem 2.6 of Drensky and Lakatos [3]. We prove that for arbitrary n ∈ N and 1 ≤ d ≤ [ 2 ] and for a field K of characteristic 2 there