Maximal arcs, codes, and new links between projective planes of order 16
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Dosyalar
Tarih
2020
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Electronic Journal Of Combinatorics
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In 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.
Açıklama
Anahtar Kelimeler
Kaynak
Electronic Journal Of Combinatorics
WoS Q Değeri
Q3
Scopus Q Değeri
Cilt
27
Sayı
1
