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The Kakeya problem : a gap in the spectrum and classification of the smallest examples

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Abstract
Kakeya sets in the affine plane are point sets that are the union of lines, one through every point on the line at infinity. The finite field Kakeya problem asks for the size of the smallest Kakeya sets and the classification of these Kakeya sets. In this article we present a new example of a small Kakeya set and we give the classification of the smallest Kakeya sets up to weight q(q + 2)/2, q/4 , both in case q even.
Keywords
(q plus t _ t)-arc, Kakeya set, Dual hyperoval, Dual code of projective plane, FINITE-FIELDS, SETS, CODES, 0_2_T, SIZE

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

Chicago
Blokhuis, Aart, Maarten De Boeck, Francesco Mazzocca, and Leo Storme. 2014. “The Kakeya Problem : a Gap in the Spectrum and Classification of the Smallest Examples.” Designs Codes and Cryptography 72 (1): 21–31.
APA
Blokhuis, A., De Boeck, M., Mazzocca, F., & Storme, L. (2014). The Kakeya problem : a gap in the spectrum and classification of the smallest examples. DESIGNS CODES AND CRYPTOGRAPHY, 72(1), 21–31.
Vancouver
1.
Blokhuis A, De Boeck M, Mazzocca F, Storme L. The Kakeya problem : a gap in the spectrum and classification of the smallest examples. DESIGNS CODES AND CRYPTOGRAPHY. 2014;72(1):21–31.
MLA
Blokhuis, Aart et al. “The Kakeya Problem : a Gap in the Spectrum and Classification of the Smallest Examples.” DESIGNS CODES AND CRYPTOGRAPHY 72.1 (2014): 21–31. Print.
@article{4407005,
  abstract     = {Kakeya sets in the affine plane are point sets that are the union of lines, one through every point on the line at infinity. The finite field Kakeya problem asks for the size of the smallest Kakeya sets and the classification of these Kakeya sets. In this article we present a new example of a small Kakeya set and we give the classification of the smallest Kakeya sets up to weight q(q + 2)/2, q/4 , both in case q even.},
  author       = {Blokhuis, Aart and De Boeck, Maarten and Mazzocca, Francesco and Storme, Leo},
  issn         = {0925-1022},
  journal      = {DESIGNS CODES AND CRYPTOGRAPHY},
  keywords     = {(q plus t _ t)-arc,Kakeya set,Dual hyperoval,Dual code of projective plane,FINITE-FIELDS,SETS,CODES,0_2_T,SIZE},
  language     = {eng},
  number       = {1},
  pages        = {21--31},
  title        = {The Kakeya problem : a gap in the spectrum and classification of the smallest examples},
  url          = {http://dx.doi.org/10.1007/s10623-012-9790-3},
  volume       = {72},
  year         = {2014},
}

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