dc.contributor.author Gildea, Joe dc.contributor.author Kaya, Abidin dc.contributor.author Roberts, Adam dc.contributor.author Taylor, Rhian dc.contributor.author Tylyshchak, Alexander dc.date.accessioned 2021-07-22T09:59:43Z dc.date.available 2021-07-22T09:59:43Z dc.date.issued 2021-09-01 dc.identifier https://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.citation Gildea, 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.2021039 en_US dc.identifier.issn 1930-5346 dc.identifier.doi 10.3934/amc.2021039 dc.identifier.uri http://hdl.handle.net/10034/625330 dc.description This 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.2021039 en_US dc.description.abstract In 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.publisher American Institute of Mathematical Sciences en_US dc.relation.url https://www.aimsciences.org/article/doi/10.3934/amc.2021039 dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/4.0/ en_US dc.subject combinatorial problems en_US dc.subject extremal self-dual codes en_US dc.subject codes over rings en_US dc.title New Self-dual Codes from 2 x 2 block circulant matrices, Group Rings and Neighbours of Neighbours en_US dc.type Article en_US dc.identifier.eissn 1930-5338 en_US dc.contributor.department University of Chester; Harmony Public Schools; Uzhgorod National University en_US dc.identifier.journal Advances in Mathematics of Communications 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.licenseref.startdate 2022-09-07 dcterms.dateAccepted 2021-07-11 rioxxterms.publicationdate 2021-09-01 dc.date.deposited 2021-07-22 en_US
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