Bulletin of the
Korean Mathematical Society BKMS

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 $\mathbb F_2 +u\mathbb F_2$ of lengths $25$ and $26$.

Keywords: automorphism, extremal code, optimal code, self-dual code

MSC numbers: Primary 94B05; Secondary 11T71