Construction and decoding of generalized skew-evaluation codes

Abstract

Skew polynomials are elements of a noncommutative ring that, in recent years, have found applications in coding theory and cryptography. Skew polynomials have a well-defined evaluation map. This map leads to the definition of a class of codes called Generalized Skew-Evaluation codes that contains Gabidulin codes as a special case as well as other related codes with additional desirable properties. A Berlekamp-Welch-type decoder for an important class of these codes can be constructed using Kötter interpolation in skew polynomial rings.