q-ary Propelinear Perfect Codes from the Regular Subgroups of the GA(r,q) and Their Ranks

Abstract: We propose a new method of constructing q-ary propelinear perfect codes. The approach utilizes permutations of the fixed length q-ary vectors that arise from the automorphisms of the regular subgroups of the affine group. For any prime q it is shown that the new class contains an infinite series of q-ary propelinear perfect codes of varying ranks of growing length.