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dc.contributor.authorGildea, Joe
dc.contributor.authorKaya, Abidin
dc.contributor.authorRoberts, Adam
dc.contributor.authorTaylor, Rhian
dc.contributor.authorTylyshchak, Alexander
dc.date.accessioned2021-07-22T09:59:43Z
dc.date.available2021-07-22T09:59:43Z
dc.date.issued2021-09-01
dc.identifierhttps://chesterrep.openrepository.com/bitstream/handle/10034/625330/New%20Self-dual%20Codes%20from%202%20x%202%20block%20circulant%20matrices%2c%20Group%20Rings%20and%20Neighbours%20of%20Neighbours.pdf?sequence=1
dc.identifier.citationGildea, J., Kaya, A., Roberts, A., Taylor, R., & Tylyshchak, A. (2021). New self-dual codes from 2 x 2 block circulant matrices, group rings and neighbours of neighbours. Advances in Mathematics of Communications, https://doi.org/10.3934/amc.2021039en_US
dc.identifier.issn1930-5346
dc.identifier.doi10.3934/amc.2021039
dc.identifier.urihttp://hdl.handle.net/10034/625330
dc.descriptionThis document is the Accepted Manuscript version of a published work that appeared in final form in Advances in Mathematics of Communications. To access the final edited and published work see http://dx.doi.org/10.3934/amc.2021039en_US
dc.description.abstractIn this paper, we construct new self-dual codes from a construction that involves a unique combination; $2 \times 2$ block circulant matrices, group rings and a reverse circulant matrix. There are certain conditions, specified in this paper, where this new construction yields self-dual codes. The theory is supported by the construction of self-dual codes over the rings $\FF_2$, $\FF_2+u\FF_2$ and $\FF_4+u\FF_4$. Using extensions and neighbours of codes, we construct $32$ new self-dual codes of length $68$. We construct 48 new best known singly-even self-dual codes of length 96.en_US
dc.publisherAmerican Institute of Mathematical Sciencesen_US
dc.relation.urlhttps://www.aimsciences.org/article/doi/10.3934/amc.2021039
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.subjectcombinatorial problemsen_US
dc.subjectextremal self-dual codesen_US
dc.subjectcodes over ringsen_US
dc.titleNew Self-dual Codes from 2 x 2 block circulant matrices, Group Rings and Neighbours of Neighboursen_US
dc.typeArticleen_US
dc.identifier.eissn1930-5338en_US
dc.contributor.departmentUniversity of Chester; Harmony Public Schools; Uzhgorod National Universityen_US
dc.identifier.journalAdvances in Mathematics of Communicationsen_US
or.grant.openaccessYesen_US
rioxxterms.funderunfundeden_US
rioxxterms.identifier.projectunfundeden_US
rioxxterms.versionAMen_US
rioxxterms.licenseref.startdate2022-09-07
dcterms.dateAccepted2021-07-11
rioxxterms.publicationdate2021-09-01
dc.date.deposited2021-07-22en_US


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