Skew Coding and Skew Factorisation

Abstract

The thesis consists of two parts. First part is on coding theory, more specifically on skew codes. It starts with a short introduction to coding theory by presenting a few codes and giving bounds on their quality. It also includes an overview of papers by Boucher and Ulmer on cyclic codes over skew polynomial rings that motivated the thesis. The second part deals with factorisation in skew polynomial rings. We improve the estimate of the bound of a polynomial in skew rings given by Boucher and Ulmer and present a new approach to factorisation using difference operators.