New binary self-dual codes of lengths 50–60

Using a method for constructing binary self-dual codes with an automorphism of odd prime order p , we give a full classification of all optimal binary self-dual [ 50 + 2 t , 25 + t ] codes having an automorphism of order 5 for t = 0 , ⋯ , 5 . As a consequence, we determine the weight enumerators for which there is an optimal binary self-dual [ 52 , 26 , 10 ] code. Some of the constructed codes for lengths 52, 54, 58, and 60 have new values for the parameter in their weight enumerator. We also construct more than 3,000 new doubly-even [ 56 , 28 , 12 ] self-dual codes.