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Nested Construction of ℤ2L-Linear Codes

dc.contributor.authorBastos, Gustavo T.
dc.contributor.authorBollauf, Maiara F.
dc.contributor.authorFerrari, Agnaldo J. [UNESP]
dc.contributor.authorYtrehus, Oyvind
dc.contributor.institutionFederal University of São João Del-Rei
dc.contributor.institutionSimula UiB
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.date.accessioned2025-04-29T19:33:49Z
dc.date.issued2024-01-01
dc.description.abstractWe present novel techniques to verify the linearity of ℤ2L-linear codes, i.e., the binary codes obtained as the image of the generalized Gray map of ℤ2L-additive codes. The central idea is the definition of two auxiliary binary codes, which we denote by associated and decomposition codes. Since ℤ2L-linear codes can be linear or nonlinear, as a consequence of our contributions, we are able to construct families of linear ℤ2L-linear codes from nested Reed-Muller and cyclic codes. This work expands on previous results from the literature, where the linearity of ℤ2L. linear codes was established with respect to the kernel of the underlying ℤ2L-additive code and/or operations on ℤ2L.en
dc.description.affiliationFederal University of São João Del-Rei, MG
dc.description.affiliationSimula UiB
dc.description.affiliationSão Paulo State University (Unesp) School of Sciences, SP
dc.description.affiliationUnespSão Paulo State University (Unesp) School of Sciences, SP
dc.format.extent2598-2603
dc.identifierhttp://dx.doi.org/10.1109/ISIT57864.2024.10619235
dc.identifier.citationIEEE International Symposium on Information Theory - Proceedings, p. 2598-2603.
dc.identifier.doi10.1109/ISIT57864.2024.10619235
dc.identifier.issn2157-8095
dc.identifier.scopus2-s2.0-85202902333
dc.identifier.urihttps://hdl.handle.net/11449/304065
dc.language.isoeng
dc.relation.ispartofIEEE International Symposium on Information Theory - Proceedings
dc.sourceScopus
dc.titleNested Construction of ℤ2L-Linear Codesen
dc.typeTrabalho apresentado em eventopt
dspace.entity.typePublication
relation.isOrgUnitOfPublicationaef1f5df-a00f-45f4-b366-6926b097829b
relation.isOrgUnitOfPublication.latestForDiscoveryaef1f5df-a00f-45f4-b366-6926b097829b
unesp.campusUniversidade Estadual Paulista (UNESP), Faculdade de Ciências, Baurupt

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