On $q$-ary propelinear perfect codes based on regular subgroups of the general affine group

A code is said to be propelinear if its automorphism group contains a subgroup acting on its codewords regularly. A subgroup of the group $GA(r,q)$ of affine transformations is said to be regular if it acts regularly on vectors of $\mathbb{F}_q^r$. Every automorphism of a regular subgroup of the general affine group $GA(r,q)$ induces a permutation on the cosets of the Hamming code of length $\frac{q^r-1}{q-1}$ . Based on this permutation, we propose a construction of $q$-ary propelinear perfect codes of length $\frac{q^{r+1}-1}{q-1}$. In particular, for any prime $q$ we obtain an infinite series of almost full rank $q$-ary propelinear perfect codes.