Maximal arcs in projective planes of order 16 and related designs
Yükleniyor...
Dosyalar
Tarih
2019
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Walter De Gruyter Gmbh
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The 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.
Açıklama
Anahtar Kelimeler
Maximal arc, projective plane, resolvable design
Kaynak
Advances in Geometry
WoS Q Değeri
Q3
Scopus Q Değeri
Cilt
19
Sayı
3
