Some new extremal codes of lengths 76 and 78
We find new extremal [76, 38, 14] and (78, 39, 14] binary self-dual codes. The code of length 76 is the first known self-dual code with these parameters. It is shadow extremal and the shortest known self-dual code with minimal distance 14. It has an automorphism of order 19 without fixed coordinates. The code of length 78 has a new weight enumerator and an automorphism of order 19 with two fixed coordinates.
extremal codes binary self-dual codes automorphism of codes