Dougherty, StevenGildea, JoeKorban, AdrianKaya, Abidin2020-03-032020-03-032020-10-13Dougherty, S., Gildea, J., Korban, A. & Kaya, A. (2020). New extremal self-dual binary codes of length 68 via composite construction, F2 + uF2 lifts, extensions and neighbors. International Journal of Information and Coding Theory, 5(3-4), 211-226. https://doi.org/10.1504/IJICOT.2020.11070310.1504/IJICOT.2020.110703http://hdl.handle.net/10034/623218We 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 + uF2, to obtain extremal binary images of codes of length 64. Finally, we use the extension method and neighbor 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.https://creativecommons.org/licenses/by-nc-nd/4.0/Group ringsSelf-dual codesCodes over ringsArticle1753-7711International Journal of Information and Coding Theory