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For any integer Â¿ Â¿ 1 and for any prime power q , an explicit construction of an infinite family of completely regular (and completely transitive) q-ary codes with d = 3 and with covering radius Â¿ 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 Â¿, which are not completely regular, is also given. In both constructions, the Kronecker product is the basic tool that has been used.