Using representation theoretical methods we investigate self-dual group codes and their extensions in characteristic 2. We prove that the existence of a self-dual extended group code heavily depends on a particular structure of the group algebra KG which can be checked by an easy-to-handle criteria in elementary number theory. Surprisingly, in the binary… (More)
There is the long-standing question whether the class of cyclic codes is asymptotically good. By an old result of Lin and Weldon, long Bose-Chaudhuri-Hocquenhem (BCH) codes are asymptotically bad. Berman proved that cyclic codes are asymptotically bad if only finitely many primes are involved in the lengths of the codes. We investigate further classes of… (More)
General arguments of Baumslag and Bieri guarantee that any torsion-free finitely generated metabelian group of finite Prüfer rank can be embedded in a metabelian constructible group. Here, we consider the metric behavior of a rich class of examples and analyze the distortions of specific embeddings.
In this correspondence, we prove that the class of binary self-dual doubly even 2-quasi-cyclic transitive codes is asymptotically good. This improves a recent result of Bazzi and Mitter (<i>IEEE Trans. Inf. Theory</i>, vol. 52, pp. 3210-3219, 2006). The proof is based on the study of a particular class of codes invariant under dihedral groups using a blend… (More)