Group matrix ring codes and constructions of self-dual codes
dc.authorid | https://orcid.org/0000-0002-2084-6260 | en_US |
dc.authorid | https://orcid.org/0000-0002-5229-4018 | en_US |
dc.authorscopusid | 55420759300 | en_US |
dc.authorscopusid | 36728602600 | en_US |
dc.authorwosid | ABB-4228-2020 | en_US |
dc.authorwosid | GQB-3301-2022 | en_US |
dc.contributor.author | Dougherty, S. T. | |
dc.contributor.author | Korban, Adrian | |
dc.contributor.author | Şahinkaya, Serap | |
dc.contributor.author | Üstün, Deniz | |
dc.date.accessioned | 2023-08-29T08:57:08Z | |
dc.date.available | 2023-08-29T08:57:08Z | |
dc.date.issued | 2023 | en_US |
dc.department | Fakülteler, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü | en_US |
dc.description.abstract | In 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. | en_US |
dc.identifier.citation | Dougherty, 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 | en_US |
dc.identifier.doi | https://doi.org/10.1007/s00200-021-00504-9. | en_US |
dc.identifier.endpage | 299 | en_US |
dc.identifier.issue | 2 | en_US |
dc.identifier.startpage | 279 | en_US |
dc.identifier.uri | https://doi.org/10.1007/s00200-021-00504-9 | |
dc.identifier.uri | https://hdl.handle.net/20.500.13099/171 | |
dc.identifier.volume | 34 | en_US |
dc.identifier.wos | WOS:000636185000001 | en_US |
dc.identifier.wosquality | Q4 | en_US |
dc.institutionauthor | Şahinkaya, Serap | |
dc.institutionauthor | Üstün, Deniz | |
dc.language.iso | eng | en_US |
dc.publisher | Springer Link | en_US |
dc.relation.ispartof | Applicable Algebra in Engineering, Communication and Computing | en_US |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
dc.rights | info:eu-repo/semantics/openAccess | en_US |
dc.subject | Group Matrix Rings | en_US |
dc.subject | Linear Codes | en_US |
dc.subject | Self-Dual Codes | en_US |
dc.subject | Codes over Rings | en_US |
dc.title | Group matrix ring codes and constructions of self-dual codes | en_US |
dc.type | article | en_US |
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