dc.contributor.author Gildea, Joe dc.contributor.author Kaya, Abidin dc.contributor.author Korban, Adrian dc.contributor.author Yildiz, Bahattin dc.date.accessioned 2020-07-22T08:32:14Z dc.date.available 2020-07-22T08:32:14Z dc.identifier https://chesterrep.openrepository.com/bitstream/handle/10034/623555/New%20Extremal%20binary%20self-dual%20codes%20of%20length%2068%20from%20generalized%20neighbors.pdf?sequence=1 dc.identifier.citation Gildea, 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. en_US dc.identifier.doi 10.1016/j.ffa.2020.101727 dc.identifier.uri http://hdl.handle.net/10034/623555 dc.description.abstract In 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 $W_{68,2}$. en_US dc.publisher Elsevier en_US dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/4.0/ en_US dc.subject Extremal self-dual codes en_US dc.subject Neighbor en_US dc.subject Distance of self-dual codes en_US dc.subject Weight enumerator en_US dc.title New Extremal binary self-dual codes of length 68 from generalized neighbors en_US dc.type Article en_US dc.contributor.department University of Chester; Sampoerna University; Northern Arizona University en_US dc.identifier.journal Finite Fields and their Applications en_US or.grant.openaccess Yes en_US rioxxterms.funder unfunded en_US rioxxterms.identifier.project unfunded en_US rioxxterms.version AM en_US rioxxterms.versionofrecord https://doi.org/10.1016/j.ffa.2020.101727 rioxxterms.licenseref.startdate 2021-07-30 rioxxterms.publicationdate 2020-07-30 dc.dateAccepted 2020-07-12 dc.date.deposited 2020-07-22 en_US dc.indentifier.issn 1071-5797 en_US
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