Maximal arcs in projective planes of order 16 and related designs

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dc.authorid0000-0001-5488-9341
dc.authorid0000-0003-1806-3571
dc.authorwosidGezek, Mustafa/AAW-3807-2020
dc.contributor.authorGezek, Mustafa
dc.contributor.authorTonchev, Vladimir D.
dc.contributor.authorWagner, Tim
dc.date.accessioned2022-05-11T14:31:24Z
dc.date.available2022-05-11T14:31:24Z
dc.date.issued2019
dc.departmentFakülteler, Fen Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractThe resolutions and maximal sets of compatible resolutions of all 2-(120,8,1) designs arising from maximal (120,8)-arcs, and the 2-(52, 4, 1) designs arising from previously known maximal (52, 4)-arcs, as well as some newly discovered maximal (52, 4)-arcs in the known projective planes of order 16, are computed. It is shown that each 2-(1.20,8,1) design associated with a maximal (1.20,8)-arc is embeddable in a unique way in a projective plane of order 16. This result suggests a possible strengthening of the Bose-Shrikhande theorem about the embeddability of the complement of a hyperoval in a projective plane of even order. The computations of the maximal sets of compatible resolutions of the 2-(52, 4, 1) designs associated with maximal (52,4)-arcs show that five of the known projective planes of order 16 contain maximal arcs whose associated designs are embeddable in two nonisomorphic planes of order 16.
dc.description.sponsorshipNSANational Security Agency [H98230-16-1-0011]
dc.description.sponsorshipResearch supported by NSA Grant H98230-16-1-0011.
dc.identifier.doi10.1515/advgeom-2018-0002
dc.identifier.endpage351
dc.identifier.issn1615-715X
dc.identifier.issn1615-7168
dc.identifier.issue3en_US
dc.identifier.startpage345
dc.identifier.urihttps://doi.org/10.1515/advgeom-2018-0002
dc.identifier.urihttps://hdl.handle.net/20.500.11776/7439
dc.identifier.volume19
dc.identifier.wosWOS:000475296100006
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.institutionauthorGezek, Mustafa
dc.language.isoen
dc.publisherWalter De Gruyter Gmbh
dc.relation.ispartofAdvances in Geometry
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectMaximal arc
dc.subjectprojective plane
dc.subjectresolvable design
dc.titleMaximal arcs in projective planes of order 16 and related designs
dc.typeArticle

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