Families of twisted tensor product codes

Using geometric properties of the
variety $\cV_{r,t}$, the image
under the Grassmannian map
of a Desarguesian $(t-1)$-spread of $\PG(rt-1,q)$,
we introduce error correcting codes related to
the twisted tensor product construction, producing several families of
constacyclic codes. We determine the precise
parameters of these codes and
characterise the words of minimum weight.