Group matrix ring codes and constructions of self-dual codes

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dc.authoridhttps://orcid.org/0000-0002-2084-6260
dc.authoridhttps://orcid.org/0000-0002-5229-4018
dc.authorscopusid55420759300
dc.authorscopusid36728602600
dc.authorwosidABB-4228-2020
dc.authorwosidGQB-3301-2022
dc.contributor.authorDougherty, S. T.
dc.contributor.authorKorban, Adrian
dc.contributor.authorŞahinkaya, Serap
dc.contributor.authorÜstün, Deniz
dc.date.accessioned2023-08-29T08:57:08Z
dc.date.available2023-08-29T08:57:08Z
dc.date.issued2023
dc.departmentFakülteler, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü
dc.description.abstractIn this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring M-k(R) and the ring R, where R is the commutative Frobenius ring. We show that codes over the ring M-k(R) are one sided ideals in the group matrix ring M-k(R)G and the corresponding codes over the ring R are G(k)-codes of length kn. Additionally, we give a generator matrix for self-dual codes, which consist of the mentioned above matrix construction. We employ this generator matrix to search for binary self-dual codes with parameters [72, 36, 12] and find new singly-even and doubly-even codes of this type. In particular, we construct 16 new Type I and 4 new Type II binary [72, 36, 12] self-dual codes.
dc.identifier.citationDougherty, S. T., Korban, A, Sahinkaya, S, Ustun, D. (2023). Group matrix ring codes and constructions of self-dual codes. Applicable Algebra in Engineering Communication And Computing, 34 (2), 279-299. DOI10.1007/s00200-021-00504-9
dc.identifier.doi10.1007/s00200-021-00504-9
dc.identifier.endpage299en_US
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85132755105
dc.identifier.startpage279en_US
dc.identifier.urihttps://doi.org/10.1007/s00200-021-00504-9
dc.identifier.urihttps://hdl.handle.net/20.500.13099/171
dc.identifier.volume34en_US
dc.identifier.wosWOS:000636185000001
dc.identifier.wosqualityQ4
dc.indekslendigikaynakWeb of Science
dc.institutionauthorŞahinkaya, Serap
dc.institutionauthorÜstün, Deniz
dc.language.isoen
dc.publisherSpringer Link
dc.relation.ispartofApplicable Algebra in Engineering, Communication and Computing
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectGroup Matrix Rings
dc.subjectLinear Codes
dc.subjectSelf-Dual Codes
dc.subjectCodes over Rings
dc.titleGroup matrix ring codes and constructions of self-dual codes
dc.typeArticle

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