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 Self-dual codes and fixed-point-free permutations of order $2$ Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 1175-1186 https://doi.org/10.4134/BKMS.2014.51.4.1175Published online July 1, 2014 Hyun Jin Kim Ewha Womans University Abstract : 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 Full-Text :