On binary self-dual codes of lengths 60, 62, 64 and 66 having an automorphism of order 9
A method for constructing binary self-dual codes having an automorphism of order p(2) for an odd prime p is presented in (S. Bouyuklieva et al. IEEE. Trans. Inform. Theory, 51, 3678-3686, 2005). Using this method, we investigate the optimal self-dual codes of lengths 60 <= n <= 66 having an automorphism of order 9 with six 9-cycles, t cycles of length 3 and f fixed points. We classify all self-dual [60,30,12] and [62,31,12] codes possessing such an automorphism, and we construct many doubly-even [64,32,12] and singly-even [66,33,12] codes. Some of the constructed codes of lengths 62 and 66 are with weight enumerators for which the existence of codes was not known until now.
self-dual codes automorphims optimal codes