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A linear set view on KM-arcs

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Abstract
In this paper, we study KM-arcs of type t, i.e., point sets of size in such that every line contains 0, 2 or t of its points. We use field reduction to give a different point of view on the class of translation arcs. Starting from a particular -linear set, called an i -club, we reconstruct the projective triads, the translation hyperovals as well as the translation arcs constructed by Korchmaros-Mazzocca, Gacs-Weiner and Limbupasiriporn. We show the KM-arcs of type q/4 recently constructed by Vandendriessche are translation arcs and fit in this family. Finally, we construct a family of KM-arcs of type q/4. We show that this family, apart from new examples that are not translation KM-arcs, contains all translation KM-arcs of type q/4.
Keywords
KM-arc, (0, 2, t)-arc, Set of even type, Translation arc, PLANES, ORDER, 2, T

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Please use this url to cite or link to this publication:

MLA
De Boeck, Maarten, and Geertrui Van de Voorde. “A Linear Set View on KM-arcs.” JOURNAL OF ALGEBRAIC COMBINATORICS 44.1 (2016): 131–164. Print.
APA
De Boeck, M., & Van de Voorde, G. (2016). A linear set view on KM-arcs. JOURNAL OF ALGEBRAIC COMBINATORICS, 44(1), 131–164.
Chicago author-date
De Boeck, Maarten, and Geertrui Van de Voorde. 2016. “A Linear Set View on KM-arcs.” Journal of Algebraic Combinatorics 44 (1): 131–164.
Chicago author-date (all authors)
De Boeck, Maarten, and Geertrui Van de Voorde. 2016. “A Linear Set View on KM-arcs.” Journal of Algebraic Combinatorics 44 (1): 131–164.
Vancouver
1.
De Boeck M, Van de Voorde G. A linear set view on KM-arcs. JOURNAL OF ALGEBRAIC COMBINATORICS. 2016;44(1):131–64.
IEEE
[1]
M. De Boeck and G. Van de Voorde, “A linear set view on KM-arcs,” JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 44, no. 1, pp. 131–164, 2016.
@article{8507284,
  abstract     = {In this paper, we study KM-arcs of type t, i.e., point sets of size in such that every line contains 0, 2 or t of its points. We use field reduction to give a different point of view on the class of translation arcs. Starting from a particular -linear set, called an i -club, we reconstruct the projective triads, the translation hyperovals as well as the translation arcs constructed by Korchmaros-Mazzocca, Gacs-Weiner and Limbupasiriporn. We show the KM-arcs of type q/4 recently constructed by Vandendriessche are translation arcs and fit in this family. Finally, we construct a family of KM-arcs of type q/4. We show that this family, apart from new examples that are not translation KM-arcs, contains all translation KM-arcs of type q/4.},
  author       = {De Boeck, Maarten and Van de Voorde, Geertrui},
  issn         = {0925-9899},
  journal      = {JOURNAL OF ALGEBRAIC COMBINATORICS},
  keywords     = {KM-arc,(0,2,t)-arc,Set of even type,Translation arc,PLANES,ORDER,2,T},
  language     = {eng},
  number       = {1},
  pages        = {131--164},
  title        = {A linear set view on KM-arcs},
  url          = {http://dx.doi.org/10.1007/s10801-015-0661-7},
  volume       = {44},
  year         = {2016},
}

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