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The hyperplanes of the near hexagon related to the extended ternary Golay code

Bart De Bruyn (UGent) and Sergey Shpectorov
(2019) GEOMETRIAE DEDICATA. 202(1). p.9-26
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Abstract
We prove that the near hexagon associated with the extended ternary Golay code has, up to isomorphism, 25 hyperplanes, and give an explicit construction for each of them. As a main tool in the proof, we show that the classification of these hyperplanes is equivalent to the determination of the orbits on vectors of certain modules for the group 2 center dot M-12.
Keywords
Extended ternary Golay code, Near hexagon, Hyperplane, Mathieu group M-12, POLYGONS

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

MLA
De Bruyn, Bart, and Sergey Shpectorov. “The Hyperplanes of the near Hexagon Related to the Extended Ternary Golay Code.” GEOMETRIAE DEDICATA, vol. 202, no. 1, 2019, pp. 9–26, doi:10.1007/s10711-018-0400-z.
APA
De Bruyn, B., & Shpectorov, S. (2019). The hyperplanes of the near hexagon related to the extended ternary Golay code. GEOMETRIAE DEDICATA, 202(1), 9–26. https://doi.org/10.1007/s10711-018-0400-z
Chicago author-date
De Bruyn, Bart, and Sergey Shpectorov. 2019. “The Hyperplanes of the near Hexagon Related to the Extended Ternary Golay Code.” GEOMETRIAE DEDICATA 202 (1): 9–26. https://doi.org/10.1007/s10711-018-0400-z.
Chicago author-date (all authors)
De Bruyn, Bart, and Sergey Shpectorov. 2019. “The Hyperplanes of the near Hexagon Related to the Extended Ternary Golay Code.” GEOMETRIAE DEDICATA 202 (1): 9–26. doi:10.1007/s10711-018-0400-z.
Vancouver
1.
De Bruyn B, Shpectorov S. The hyperplanes of the near hexagon related to the extended ternary Golay code. GEOMETRIAE DEDICATA. 2019;202(1):9–26.
IEEE
[1]
B. De Bruyn and S. Shpectorov, “The hyperplanes of the near hexagon related to the extended ternary Golay code,” GEOMETRIAE DEDICATA, vol. 202, no. 1, pp. 9–26, 2019.
@article{8667899,
  abstract     = {{We prove that the near hexagon associated with the extended ternary Golay code has, up to isomorphism, 25 hyperplanes, and give an explicit construction for each of them. As a main tool in the proof, we show that the classification of these hyperplanes is equivalent to the determination of the orbits on vectors of certain modules for the group 2 center dot M-12.}},
  author       = {{De Bruyn, Bart and Shpectorov, Sergey}},
  issn         = {{0046-5755}},
  journal      = {{GEOMETRIAE DEDICATA}},
  keywords     = {{Extended ternary Golay code,Near hexagon,Hyperplane,Mathieu group M-12,POLYGONS}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{9--26}},
  title        = {{The hyperplanes of the near hexagon related to the extended ternary Golay code}},
  url          = {{http://dx.doi.org/10.1007/s10711-018-0400-z}},
  volume       = {{202}},
  year         = {{2019}},
}
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