LAUSR

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.