Construction of Automorphism Groups of Hamming Codes Ā₇ and A₈

The automorphism group of a code is useful in the study of equivalence classes of codes. In this paper, I use some methods to construct automorphism groups of Hamming codes Ā₇ and A₈ respectively. Hamming codes Ā₇ and A₈ are self-orthogonal codes, and A₈ is also self-dual. I prove that the automorphism group of Ā₇ and linear transformation group GL₃(2) to be isomorphism, and then I extend code Ā₇ to [8, 4] code. Finally I construct the automorphism group of Hamming code A₈ on the basis of group Aut(Ā₇).