Maximal arcs, codes, and new links between projective planes of order 16

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dc.authorid0000-0001-5488-9341
dc.authorwosidGezek, Mustafa/AAW-3807-2020
dc.contributor.authorGezek, Mustafa
dc.contributor.authorMathon, Rudi
dc.contributor.authorTonchev, Vladimir D.
dc.date.accessioned2022-05-11T14:04:41Z
dc.date.available2022-05-11T14:04:41Z
dc.date.issued2020
dc.departmentFakülteler, Fen Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractIn this paper we consider binary linear codes spanned by incidence matrices of Steiner 2-designs associated with maximal arcs in projective planes of even order, and their dual codes. Upper and lower bounds on the 2-rank of the incidence matrices are derived. A lower bound on the minimum distance of the dual codes is proved, and it is shown that the bound is achieved if and only if the related maximal arc contains a hyperoval of the plane. The binary linear codes of length 52 spanned by the incidence matrices of 2-(52, 4, 1) designs associated with previously known and some newly found maximal arcs of degree 4 in projective planes of order 16 are analyzed and classified up to equivalence. The classification shows that some designs associated with maximal arcs in nonisomorphic planes generate equivalent codes. This phenomenon establishes new links between several of the known planes. A conjecture concerning the codes of maximal arcs in PG(2, 2(m)) is formulated.
dc.identifier.issn1077-8926
dc.identifier.issue1en_US
dc.identifier.urihttps://hdl.handle.net/20.500.11776/4719
dc.identifier.volume27
dc.identifier.wosWOS:000521463000010
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.institutionauthorGezek, Mustafa
dc.language.isoen
dc.publisherElectronic Journal Of Combinatorics
dc.relation.ispartofElectronic Journal Of Combinatorics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.titleMaximal arcs, codes, and new links between projective planes of order 16
dc.typeArticle

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