Elation KM-Arcs

  • Maarten de BoeckEmail author
  • Geertrui van de Voorde

Mathematics Subject Classification (2010)

51E20 51E21 


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  1. [1]
    J. Bamberg, A. Betten, Ph. Cara, J. De Beule, M. Lavrauw and M. Neunhöffer: Finite Incidence Geometry, FinInG - a GAP package, version 1.3.3, 2016.Google Scholar
  2. [2]
    M. De Boeck and G. Van de Voorde: A linear set view on KM-arcs, J. Algebraic Combin. 44 (2016), 131–164.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    A. Gács and Zs. Weiner: On (q+t)-arcs of type (0;2; t), Des. Codes Cryptogr. 29 (2003), 131–139.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    M. Hall: Ovals in the Desarguesian plane of order 16, Ann. Mat. Pura Appl. 102 (1975), 159–176.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    J. D. Key, T. P. McDonough and V. C. Mavron: An upper bound for the min- imum weight of the dual codes of Desarguesian planes, European J. Combin. 30 (2009), 220–229.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    G. Korchmáros and F. Mazzocca: On (q+t)-arcs of type (0;2; t) in a desarguesian plane of order q, Math. Proc. Cambridge Philos. Soc. 108 (1990), 445–459.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    M. Lavrauw and G. Van de Voorde: Field reduction infinite geometry, Topics in finite fields, Contemp. Math., 632, Amer. Math. Soc., Providence, RI, 2010.Google Scholar
  8. [8]
    R. Lidl and H. Niederreiter: Finite Fields, second ed., Encyclopedia Math. Appl., vol. 20, Cambridge Univ. Press, Cambridge, 1997.Google Scholar
  9. [9]
    G. Migliori: Insiemi di tipo (0;2;q=2) in un piano proiettivo e sistemi di terne di Steiner, Rend. Mat. Appl. 7 (1987), 77–82.MathSciNetGoogle Scholar
  10. [10]
    O. Polverino: Linear sets in finite projective spaces, Discrete Math. 310 (2010), 3096–3107.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    C. M. O’Keefe and T. Penttila: Hyperovals in PG(2; 16), European J. Combin. 12 (1991), 51–59.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    S. E. Payne and J. E. Conklin: An unusual generalized quadrangle of order sixteen, J. Combin. Theory Ser. A 24 (1978), 50–74.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    B. Segre: Sui k-archi nei piani finiti di caratteristica due, Rev. Math. Pures Appl. 2 (1957), 289–300.MathSciNetzbMATHGoogle Scholar
  14. [14]
    P. Vandendriessche: Codes of Desarguesian projective planes of even order, projective triads and (q +t; t)-arcs of type (0;2; t), Finite Fields Appl. 17 (6) (2011), 521–531.MathSciNetzbMATHGoogle Scholar
  15. [15]
    P. Vandendriessche: A new class of (q+t; t)-arcs of type (0;2; t), talk at Giornate di geometria, Vicenza, 13–14 February 2012.Google Scholar
  16. [16]
    P. Vandendriessche: On KM-arcs in small Desarguesian planes, Electronic J. Comb. 24 (2017).Google Scholar

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Vakgroep WiskundeUniversiteit GentGentBelgium
  2. 2.School of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand

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