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 exactly determine the parameters of these codes and characterise the words of minimum weight.