Division algebras and MRD codes from skew polynomials

Let D be a division algebra, finite-dimensional over its center, and R = D[t; s, d] a skew polynomial ring. Using skew polynomials f ? R, we construct division algebras and maximum rank distance codes consisting of matrices with entries in a noncommutative division algebra or field. These include Jha Johnson semifields, and the classes of classical and twisted Gabidulin codes constructed by Sheekey.