On the self-dual codes with an automorphism of order 5

For lengths 60, 62, and 64, by applying the method for constructing self-dual codes having an automorphism of odd prime order, we classify all optimal singly even self-dual codes with an automorphism of order 5 with 12 cycles. For the binary self-dual [62, 31, 12] codes we have found five new values of the parameter in the weight enumerator thus doubling the number of know values. For length 64 we have found codes with 14 new parameter values for both known weight enumerators. By shortening all binary self-dual [60, 30, 12] codes having an automorphism of order 5 we construct many new [58, 29, 10] self-dual codes. We have found a new value of the parameter in the weight enumerator of these codes.