ON CYCLIC AND NEGACYCLIC CODES WITH ONE-DIMENSIONAL HULLS AND THEIR APPLICATIONS

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dc.contributor.authorDougherty, Steven T.
dc.contributor.authorSahinkaya, Serap
dc.date.accessioned2025-03-17T12:25:11Z
dc.date.available2025-03-17T12:25:11Z
dc.date.issued2024
dc.departmentTarsus Üniversitesi
dc.description.abstractLinear codes over finite fields with small dimensional hulls have received much attention due to their applications in cryptology and quantum computing. In this paper, we study cyclic and negacyclic codes with onedimensional hulls. We determine precisely when cyclic and negacyclic codes over finite fields with one-dimensional hulls exist. We also introduce onedimensional linear complementary pairs of cyclic and negacyclic codes. As an application, we obtain numerous optimal or near optimal cyclic codes with onedimensional hulls over different fields and, by using these codes, we present new entanglement-assisted quantum error-correcting codes (EAQECCs). In particular, some of these EAQEC codes are maximal distance separable (MDS). We also obtain one-dimensional linear complementary pairs of cyclic codes, which are either optimal or near optimal.
dc.description.sponsorship[1059B192000947]
dc.description.sponsorshipAcknowledgments. Serap Sahinkaya would like to thank T.U.B.I.T.A.K (Scien-tific and Technological Research Council of Turkey) for their support (Grant Num-ber: 1059B192000947) while writing this paper.
dc.identifier.doi10.3934/amc.2022096
dc.identifier.endpage1378
dc.identifier.issn1930-5346
dc.identifier.issn1930-5338
dc.identifier.issue5
dc.identifier.scopus2-s2.0-85181242816
dc.identifier.scopusqualityQ1
dc.identifier.startpage1364
dc.identifier.urihttps://doi.org/10.3934/amc.2022096
dc.identifier.urihttps://hdl.handle.net/20.500.13099/1535
dc.identifier.volume18
dc.identifier.wosWOS:000934620200001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherAmer Inst Mathematical Sciences-Aims
dc.relation.ispartofAdvances in Mathematics of Communications
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250316
dc.subjectAssisted Quantum Codes
dc.subjectAlgebraic Structure
dc.subjectLinear Codes
dc.subjectPermutation
dc.titleON CYCLIC AND NEGACYCLIC CODES WITH ONE-DIMENSIONAL HULLS AND THEIR APPLICATIONS
dc.typeArticle

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