Kötter interpolation in skew polynomial rings

Abstract

Skew polynomials are a noncommutative generalization of ordinary polynomials that, in recent years, have found applications in coding theory and cryptography. Viewed as functions, skew polynomials have a well-defined evaluation map; however, little is known about skew-polynomial interpolation. In this work, we apply Kotter's interpolation framework to free modules over skew polynomial rings. As a special case, we introduce a simple interpolation algorithm akin to Newton interpolation for ordinary polynomials.