A method for constructing self-dual codes with an automorphism of order 2

In this paper, we investigate binary self-dual codes with an automorphism of order 2 with c cycles and f fixed points. A method for constructing such codes using self-orthogonal codes of length c and self-dual codes of length f is presented. We apply this method to construct extremal self-dual codes of lengths 40, 42, 44, 52, 54, and 58. Some of them have weight enumerators for which self-dual codes were previously not known to exist. We prove that there do not exist self-dual [50, 25, 10] and [96, 48, 20] codes with an automorphism of order 2 with f fixed points for f>0 in their automorphism groups