Dougherty, StevenGildea, JoeKaya, AbidinKorban, AdrianTylyshchak, AlexanderYildiz, Bahattin2019-02-192019-02-192019-02-22Dougherty, S. T., Gildea, J., Korban, A., Kaya, A., Tylyshchak, A., & Yildiz, B. (2019). Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes. Finite Fields and their Applications, 57, 108-1271071-579710.1016/j.ffa.2019.02.004http://hdl.handle.net/10034/621892We introduce a bordered construction over group rings for self-dual codes. We apply the constructions over the binary field and the ring $\F_2+u\F_2$, using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary self-dual codes of lengths 20, 32, 40, 44, 52, 56, 64, 68, 88 and best known binary self-dual codes of length 72. In particular we obtain 41 new binary extremal self-dual codes of length 68 from groups of orders 15 and 33 using neighboring and extensions. All the numerical results are tabulated throughout the paper.enhttps://creativecommons.org/licenses/by-nc-nd/4.0/bordered constructionsextremal codescodes over ringself-dual codesgroup ringsArticleFinite Fields and Their Applications