Using the method for constructing binary self-dual codes with an automorphism of order square of a prime number, we have classified all binary self-dual codes with length 76 having minimum weight d = 14 via automorphism of order 9. Up to equivalence, there are six self-dual [76, 38, 14] codes with an automorphism of type 9-(8, 0, 4). All codes obtained have new values of the parameter in their weight enumerator, thus more than doubling the number of known values.

Using a method for constructing self-dual codes having an automorphism of odd prime order, we classify up to equivalence all binary self-dual codes with an automorphism of order 11 with 6 cycles and minimum distance 12. This classification gives new [72, 36, 12] codes with weight enumerator that was previously not obtained as well as many [66, 33, 12], [68, 34, 12], and [70, 35, 12] codes with new values of the parameters in their respective weight enumerators.

In this paper, we prove that there does not exist a binary self-dual doubly even code with an automorphism of order 9. To do so, we apply a method for constructing binary self-dual codes possessing an automorphism of order for an odd prime .

All binary [n,n/2] optimal self-dual codes for length 52 ≤n≤ 60 with an automorphism of order 7 or 13 are classified up to equivalence. Two of the constructed [54,27,10] codes have weight enumerators that were not previously known to exist. There are also some [58,29,10] codes with new values of the parameters in their weight enumerator.

We describe a method for constructing binary self-dual codes having an automorphism of order p/sup 2/ for an odd prime p. Using this method, we classify the optimal self-dual codes of lengths 36 /spl les/ n /spl les/ 44 and n = 54, having an automorphism of order 9. We obtain all 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.