On the structure of binary self-dual codes having an automorphism of order a square of an odd prime
We describe a method for constructing binary self-dual codes having an automorphism of order p(2) for an odd prime p. Using this method, we classify the optimal self-dual codes of lengths 36 <= n <= 44 and n = 54, having an automorphism of order 9. We obtain self-dual (56, 28, 12), (58, 29, 10), and (60, 30, 12) codes having an automorphism of order 9 without cycles of length 3. Some of the constructed codes of lengths 54, 58, and 60 have weight enumerators for which the existence of codes was not known before.
self-dual codes automorphisms