Dualities over the cross product of the cyclic groups of order 2

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dc.authoridhttps://orcid.org/0000-0002-2084-6260en_US
dc.authorscopusid55420759300en_US
dc.authorscopusid26325279300en_US
dc.authorwosidABB-4228-2020en_US
dc.authorwosidCOV-5724-2022en_US
dc.contributor.authorDougherty, S.T.
dc.contributor.authorŞahinkaya, Serap
dc.date.accessioned2024-08-28T08:09:01Z
dc.date.available2024-08-28T08:09:01Z
dc.date.issued2024en_US
dc.departmentFakülteler, Mühendislik Fakültesi, Mühendislik Temel Bilimleri Bölümüen_US
dc.description.abstractWe determine the number of symmetric dualities on the s-fold cross product of the cyclic group of order 2, which is the additive group of the finite field F2s. We show that the ratio of symmetric dualities over all dualities goes to 0 as s goes to infinity.We also prove a surprising result that given any two binary codes C and D of the same length n with |C||D| = 2n, then viewing them as groups there is a symmetric duality M with CM = D, which also relates their weight enumerators as additive codes in a group via the MacWilliams relations. Using this theorem we show that any additive code in this setting can be viewed as an additive complementary dual code of length 1 with respect to some duality.en_US
dc.identifier.citationDougherty S.T. ve Şahinkaya S. (2024).Dualities over the cross product of the cyclic groups of order 2. Advances in Mathematics of Communications, 18 (5), 1531 - 1546. DOI: 10.3934/amc.2023005en_US
dc.identifier.doi10.3934/amc.2023005en_US
dc.identifier.endpage1546en_US
dc.identifier.issn1930-5346
dc.identifier.issn1930-5338
dc.identifier.issue5en_US
dc.identifier.scopus2-s2.0-85199263873en_US
dc.identifier.startpage1531en_US
dc.identifier.urihttps://hdl.handle.net/20.500.13099/373
dc.identifier.volume18en_US
dc.identifier.wos000940898900001en_US
dc.identifier.wosqualityQ3en_US
dc.institutionauthorŞahinkaya, Serap
dc.language.isoengen_US
dc.publisherAmerican Institute of Mathematical Sciencesen_US
dc.relation.ispartofAdvances in Mathematics of Communicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectAdditive codesen_US
dc.subjectdualityen_US
dc.subjectMacWilliams relationsen_US
dc.titleDualities over the cross product of the cyclic groups of order 2en_US
dc.typearticleen_US

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