On Codes Over ${\mathbb{Z}}_{p^s}$ with the Extended Lee Weight

We consider codes over ${\mathbb{Z}}_{p^s}$ with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of independence of vectors in this space. We investigate the linearity and duality of the Gray images of codes over ${\mathbb{Z}}_{p^s}$.