  In this paper we consider completely regular codes, obtained from perfect
(Hamming) codes by lifting the ground field. More exactly, for a given perfect
code C of length n=(q^m-1)/(q-1) over F_q with a parity check matrix H_m, we
define a new code C_{(m,r)} of length n over F_{q^r}, r > 1, with this parity
check matrix H_m. The resulting code C_{(m,r)} is completely regular with
covering radius R = min{r,m}. We compute the intersection numbers of such codes
and, finally, we prove that Hamming codes are the only codes that, after
lifting the ground field, result in completely regular codes.
