m-ADIC RESIDUE CODES OVER THE RING Fq[v]/(vs - v) AND THEIR APPLICATIONS TO QUANTUM CODES

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dc.authoridKÖROĞLU, Mehmet Emin/0000-0002-9173-4944
dc.authoridKuruz, Ferhat/0000-0001-6197-4958
dc.authoridSari, Mustafa/0000-0003-3666-7635
dc.contributor.authorKuruz, Ferhat
dc.contributor.authorSari, Mustafa
dc.contributor.authorKoroglu, Mehmet E.
dc.date.accessioned2024-09-11T19:53:04Z
dc.date.available2024-09-11T19:53:04Z
dc.date.issued2022
dc.departmentİstanbul Gelişim Üniversitesien_US
dc.description.abstractDue to their rich algebraic structure, cyclic codes have a great deal of significance amongst linear codes. Duadic codes are the generalization of the quadratic residue codes, a special case of cyclic codes. The m-adic residue codes are the generalization of the duadic codes. The aim of this paper is to study the structure of the m-adic residue codes over the quotient ring F-q[v]/< v(s)-v >. We determine the idempotent generators of the m-adic residue codes over F-q[v]/< v(s)-v >. We obtain some parameters of optimal m-adic residue codes over F-q[v]/< v(s)-v > with respect to Griesmer bound for rings. Furthermore, we derive a condition for m-adic residue codes over F-q [v]/< v(s)-v > to contain their dual. By making use of a preserving-orthogonality Gray map, we construct a family of quantum error correcting codes from the Gray images of dual-containing m-adic residue codes over F-q[v]/< v(s)-v > and give some examples to illustrate our findings.en_US
dc.identifier.doi10.26421/QIC22.5-6-4
dc.identifier.endpage439en_US
dc.identifier.issn1533-7146
dc.identifier.issue5-6en_US
dc.identifier.scopus2-s2.0-85130069552en_US
dc.identifier.startpage427en_US
dc.identifier.urihttps://doi.org/10.26421/QIC22.5-6-4
dc.identifier.urihttps://hdl.handle.net/11363/8049
dc.identifier.volume22en_US
dc.identifier.wosWOS:000834672400004en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.language.isoenen_US
dc.publisherRinton Press, Incen_US
dc.relation.ispartofQuantum Information & Computationen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmz20240903_Gen_US
dc.subjectm-adic residue codesen_US
dc.subjectCyclic codesen_US
dc.subjectQuadratic residue codesen_US
dc.subjectCSS constructionen_US
dc.subjectQuantum codesen_US
dc.titlem-ADIC RESIDUE CODES OVER THE RING Fq[v]/(vs - v) AND THEIR APPLICATIONS TO QUANTUM CODESen_US
dc.typeArticleen_US

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