On self-orthogonal group ring codes

Abstract

We obtain structural results about group ring codes over F[G], where F is a finite field of characteristic p > 0 and the Sylow p-subgroup of the Abelian group G is cyclic. As a special case, we characterize cyclic codes over finite fields in the case the length of the code is divisible by the characteristic of the field. By the same approach we study cyclic codes of length m over the ring R = F q [u], u r = 0 with r > 0, gcd(m, q) = 1. Finally, we give a construction of quasi-cyclic codes over finite fields.