New extremal self-dual binary codes of length 68 via composite construction, 𝔽2 + u𝔽2 lifts, extensions and neighbours. (13th October 2020) - Dougherty, Steven T.; Gildea, Joe; Korban, Adrian; Kaya, Abidin
We describe a composite construction from group rings where the groups have orders 16 and 8. This construction is then applied to find the extremal binary self-dual codes with parameters [32, 16, 8] or [32, 16, 6]. We also extend this composite construction by expanding the search field which enables us to find more extremal binary self-dual codes with the above parameters and with different orders of automorphism groups. These codes are then lifted to 𝔽2 + u 𝔽2, to obtain extremal binary images of codes of length 64. Finally, we use the extension method and neighbour construction to obtain new extremal binary self-dual codes of length 68. As a result, we obtain 28 new codes of length 68 which were not known in the literature before.