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dc.contributor.authorDougherty, Steven T.
dc.contributor.authorGildea, Joe
dc.contributor.authorKorban, Adrian
dc.contributor.authorKorban, Adrian
dc.contributor.authorRoberts, Adam
dc.date.accessioned2024-02-12T02:25:14Z
dc.date.available2024-02-12T02:25:14Z
dc.date.issued2024-02-09
dc.identifierhttps://chesterrep.openrepository.com/bitstream/handle/10034/628486/R32final_v2.pdf?sequence=2
dc.identifier.citationDougherty, S. T., Gildea, J., Korban, A., & Roberts, A. M. (2024). Codes over a ring of order 32 with two Gray maps. Finite Fields and Their Applications, 95, 102384. https://doi.org/10.1016/j.ffa.2024.102384
dc.identifier.issn1071-5797
dc.identifier.doi10.1016/j.ffa.2024.102384
dc.identifier.urihttp://hdl.handle.net/10034/628486
dc.description.abstractWe describe a ring of order 32 and prove that it is a local Frobenius ring. We study codes over this ring and we give two distinct non-equivalent linear orthogonality-preserving Gray maps to the binary space. Self-dual codes are studied over this ring as well as the binary self-dual codes that are the Gray images of those codes. Specifically, we show that the image of a self-dual code over this ring is a binary self-dual code with an automorphism consisting of 2n transpositions for the first map and n transpositions for the second map. We relate the shadows of binary codes to additive codes over the ring. As Gray images of codes over the ring, binary self-dual [ 70 , 35 , 12 ] codes with 91 distinct weight enumerators are constructed for the first time in the literature.
dc.publisherElsevier
dc.relation.urlhttps://www.sciencedirect.com/science/article/pii/S1071579724000248?via%3Dihub
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectCodes over rings
dc.subjectGray maps
dc.subjectExtremal codes
dc.subjectBest known
dc.titleCodes over a ring of order 32 with two Gray maps
dc.typeArticle
dc.identifier.journalFinite Fields and Their Applications
dc.date.updated2024-02-12T02:25:14Z
dc.date.accepted2024-01-29


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