Self-dual codes and fixed-point-free permutations of order 2

We construct new binary optimal self-dual codes of length 50. We develop a construction method for binary self-dual codes with a fixed-point-free automorphism of order 2. Using this method, we find new binary optimal self-dual codes of length 52. From these codes, we obtain Lee-optimal self-dual codes over the ring F₂ + uF₂ of lengths 25 and 26.