G-codes, self-dual G-codes and reversible G-codes over the ring Bj,k

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dc.authoridGildea, Joe/0000-0001-7242-779X
dc.authoridKorban, Adrian/0000-0001-5206-6480
dc.authoridSahinkaya, Serap/0000-0002-2084-6260
dc.contributor.authorDougherty, S. T.
dc.contributor.authorGildea, Joe
dc.contributor.authorKorban, Adrian
dc.contributor.authorSahinkaya, Serap
dc.date.accessioned2025-03-17T12:27:29Z
dc.date.available2025-03-17T12:27:29Z
dc.date.issued2021
dc.departmentTarsus Üniversitesi
dc.description.abstractIn this work, we study a new family of rings, B-j,B-k,B- whose base field is the finite field F-pr. We study the structure of this family of rings and show that each member of the family is a commutative Frobenius ring. We define a Gray map for the new family of rings, study Gcodes, self-dual G-codes, and reversible G-codes over this family. In particular, we show that the projection of a G-code over B-j,B-k to a code over B-l,B-m is also a G-code and the image under the Gray map of a self-dual G-code is also a self-dual G-code when the characteristic of the base field is 2. Moreover, we show that the image of a reversible G-code under the Gray map is also a reversible G2(j+k)-code. The Gray images of these codes are shown to have a rich automorphism group which arises from the algebraic structure of the rings and the groups. Finally, we show that quasi- G codes, which are the images of G-codes under the Gray map, are also G(s)-codes for some s.
dc.identifier.doi10.1007/s12095-021-00487-x
dc.identifier.endpage616
dc.identifier.issn1936-2447
dc.identifier.issn1936-2455
dc.identifier.issue5
dc.identifier.scopus2-s2.0-85105414440
dc.identifier.scopusqualityQ2
dc.identifier.startpage601
dc.identifier.urihttps://doi.org/10.1007/s12095-021-00487-x
dc.identifier.urihttps://hdl.handle.net/20.500.13099/2287
dc.identifier.volume13
dc.identifier.wosWOS:000646509000002
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofCryptography and Communications-Discrete-Structures Boolean Functions and Sequences
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250316
dc.subjectCodes over rings
dc.subjectGray maps
dc.subjectSelf-dual codes
dc.subjectAutomorphism groups
dc.titleG-codes, self-dual G-codes and reversible G-codes over the ring Bj,k
dc.typeArticle

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