Algebraic Methods in Coding Theory

This research school intends to present to the participants (mainly Ph.D. students) applications of commutative and non-commutative algebra to coding theory. Thus we will have courses and talks on the following topics (but not limited to them):

• The broad use of techniques from finite group algebras to study, among others, cyclic, abelian and metacyclic codes;
• Evaluation codes constructed from ideals in polynomial rings;
• Applications of Gröbner basis methods to the estimation or computing of code parameters and decoding;
• Applications of results from Hilbert functions and regularity of ideals to the estimation or computing of code parameters;
• Convolutional codes;
• Applications of numerical semigoups theory to coding theory;
• Codes over rings.

The main motivation of this school is to introduce students to coding theory as an area of research. We expect students firstly to understand the basics of coding theory, and then to get a working knowledge of some methods coming from both commutative and non-commutative algebra which are currently being applied successfully to study a variety of codes. Our aim is to prepare students to pursue research in this area, by using the tools described in the short courses and talks. A second motivation for this school is to promote the exchange of experiences among researchers and students from different parts of the country and from abroad.