Gildea, JoeKaya, AbidinTaylor, RhianYildiz, Bahattin2018-01-242018-01-242018-02-03Gildea, J., Kaya, A., Taylor, R., & Yildiz, B. (2018). Constructions for Self-Dual Codes Induced from Group Rings, to appear in Finite Fields and Their Applications, 51, 71-92. https://doi.org/10.1016/j.ffa.2018.01.0021071-579710.1016/j.ffa.2018.01.002http://hdl.handle.net/10034/620815In this work, we establish a strong connection between group rings and self-dual codes. We prove that a group ring element corresponds to a self-dual code if and only if it is a unitary unit. We also show that the double-circulant and four-circulant constructions come from cyclic and dihedral groups, respectively. Using groups of order 8 and 16 we find many new construction methods, in addition to the well-known methods, for self-dual codes. We establish the relevance of these new constructions by finding many extremal binary self-dual codes using them, which we list in several tables. In particular, we construct 10 new extremal binary self-dual codes of length 68.enhttp://creativecommons.org/licenses/by-nc-nd/4.0/Group ringsSelf-dual codesCodes over ringsArticleFinite Fields and Their Applications