Self-dual codes over F-2 x (F-2 + vF(2))

Abstract

In this study we consider Euclidean and Hermitian self-dual codes over the direct product ring F-2 x (F-2 + vF(2)) where v(2) = v. We obtain some theoretical outcomes about self-dual codes via the generator matrices of free linear codes over F-2 x(F-2 + vF(2)). Also, we obtain upper bounds on the minimum distance of linear codes for both the Lee distance and the Gray distance. Moreover, we find some free Euclidean and free Hermitian self-dual codes over F-2 x (F-2 + vF(2)) via some useful construction methods.