Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours

Gildea, Joe; Korban, Adrian; Roberts, Adam; Tylyshchak, Alexander

dc.contributor.author	Gildea, Joe
dc.contributor.author	Korban, Adrian
dc.contributor.author	Roberts, Adam
dc.contributor.author	Tylyshchak, Alexander
dc.date.accessioned	2022-04-11T01:01:07Z
dc.date.available	2022-04-11T01:01:07Z
dc.date.issued	2022-04-01
dc.identifier	https://chesterrep.openrepository.com/bitstream/handle/10034/626799/AMC%20Accepted.pdf?sequence=2
dc.identifier.citation	Gildea, J., Korban, A., Roberts, A. M., & Tylyshchak, A. (2024). Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours. Advances in Mathematics of Communications, 18(3), 738-75. https://doi.org/10.3934/amc.2022021
dc.identifier.issn	1930-5346
dc.identifier.doi	10.3934/amc.2022021
dc.identifier.uri	http://hdl.handle.net/10034/626799
dc.description	This article has been accepted for publication in a revised form in [Advances in Mathematics of Communications] [https://www.aimsciences.org//article/doi/10.3934/amc.2022021]. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works
dc.description.abstract	In this work, we define a modification of a bordered construction for self-dual codes which utilises \lambda-circulant matrices. We provide the necessary conditions for the construction to produce self-dual codes over finite commutative Frobenius rings of characteristic 2. Using the modified construction together with the neighbour construction, we construct many binary self-dual codes of lengths 54, 68, 82 and 94 with weight enumerators that have previously not been known to exist.
dc.publisher	American Institute of Mathematical Sciences
dc.relation.url	https://www.aimsciences.org/article/doi/10.3934/amc.2022021
dc.rights.uri	https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.source	pissn: 1930-5346
dc.source	eissn: 1930-5338
dc.subject	Applied Mathematics
dc.subject	Discrete Mathematics and Combinatorics
dc.subject	Computer Networks and Communications
dc.subject	Algebra and Number Theory
dc.subject	Microbiology
dc.title	Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours
dc.type	Article
dc.identifier.eissn	1930-5338
dc.contributor.department	Dundalk Institute of Technology; University of Chester; Ferenc Rákóczi II Transcarpathian Hungarian College of Higher Education
dc.identifier.journal	Advances in Mathematics of Communications
dc.date.updated	2022-04-11T01:01:06Z
dc.date.accepted	2022-02
rioxxterms.version	AM