  Let $D$ be a division algebra, finite-dimensional over its center, and
$R=D[t;\sigma,\delta]$ a skew polynomial ring. Using skew polynomials $f\in R$,
we construct division algebras and a generalization of maximum rank distance
codes consisting of matrices with entries in a noncommutative division algebra
or field. These include a class of codes constructed by Sheekey (in particular,
generalized Gabidulin codes), as well as Jha Johnson semifields.
