  In this article we construct a new family of semifields, containing and
extending two well-known families, namely Albert's generalised twisted fields
and Petit's cyclic semifields (also known as Johnson-Jha semifields). The
construction also gives examples of semifields with parameters for which no
examples were previously known. In the case of semifields two dimensions over a
nucleus and four-dimensional over their centre, the construction gives all
possible examples.
  Furthermore we embed these semifields in a new family of maximum
rank-distance codes, encompassing most known current constructions, including
the (twisted) Delsarte-Gabidulin codes, and containing new examples for most
parameters.
