Functional Decomposition of a Class of wild Polynomials

Robert S. Coulter1, George Havas 1, Marie Henderson1
1Centre for Discrete Mathematics and Computing Department of Computer Science and Electrical Engineering The University of Queensland Queensland, 4072, Australia

Abstract

No general algorithm is known for the functional decomposition of wild polynomials over a finite field. However, partial solutions exist. In particular, a fast functional decomposition algorithm for linearised polynomials has been developed using factoring
methods in skew-polynomial rings. This algorithm is extended to a related class of wild polynomials, which are sub-linearised polynomials.