Extended abstract: Codes as modules over skew polynomial rings

Abstract

This talk is an overview of codes that are defined as modules over skew polynomial rings. These codes can be seen as a generalization of cyclic codes or more generally polynominal codes to a non commutative polynomial ring. Most properties of classical cyclic codes can be generalized to this new setting and self-dual codes can be easily identified. Those rings are no longer unique factorization rings, therefore there are many factors of Xn - 1, each generating a “skew cyclic code”. In previous works many new codes and new self-dual codes with a better distance than existing codes have been found. Recently cyclic and skewcyclic codes over rings have been extensively studied in order to obtain codes over subfields (or subrings) under mapping with good properties.