Skew Polynomial Rings and Codes

We will start with basic definitions of Ore extensions and briefly analyze both the arithmetic and the structure of those rings with the help of evaluations and pseudo linear transformations. We will also go through some recent papers, initiated by Panov, and defining Hopf algebra structure on a skew polynomial ring.

About 12 years ago skew polynomial rings started to be used to construct interesting codes. We will present some of these constructions and related results connected with exponents of skew polynomials. We will then consider the constructions of dual codes using some noncommuative Frobenius algebras where the skew polynomials are always implicitly present. The prerequisites will be minimal and efforts will be made to make the courses available to all the listeners.

Some exercises or problems will finish every lectures