Gildea, JoeKaya, AbidinKorban, AdrianYildiz, Bahattin2020-07-222020-07-22Gildea, J., Abidin, K., Korban, A. & Yildiz, B. (2020). New Extremal binary self-dual codes of length 68 from generalized neighbors. Finite Fields and Their Applications, 67, 101727.10.1016/j.ffa.2020.101727http://hdl.handle.net/10034/623555In this work, we use the concept of distance between self-dual codes, which generalizes the concept of a neighbor for self-dual codes. Using the $k$-neighbors, we are able to construct extremal binary self-dual codes of length 68 with new weight enumerators. We construct 143 extremal binary self-dual codes of length 68 with new weight enumerators including 42 codes with $\gamma=8$ in their $W_{68,2}$ and 40 with $\gamma=9$ in their $W_{68,2}$. These examples are the first in the literature for these $\gamma$ values. This completes the theoretical list of possible values for $\gamma$ in $W_{68,2}$.https://creativecommons.org/licenses/by-nc-nd/4.0/Extremal self-dual codesNeighborDistance of self-dual codesWeight enumeratorArticleFinite Fields and Their Applications