On q-ary propelinear codes from regular subgroups of the affine group

Based on a $q$-ary analogue of Solov'eva's construction, similarly to the binary case, a new series of $q$-ary propelinear perfect codes is found. For the obtained codes, the rank problem is partially solved. In particular, propelinear perfect codes of precomplete rank exist for length $q^2+q+1$ for all primes $q$, $q>2$.