New completely regular q-ary codes based on Kronecker products

Abstract: For any integer $\rho \geq 1$ and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d=3 and with covering radius $\rho$ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius $\rho$, which are not completely regular, is also given. In both constructions the Kronecker product is the basic tool that has been used.