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A characterization of the Grassmann embedding of H(q), with q even

An De Wispelaere (UGent) , Joseph Thas (UGent) and Hendrik Van Maldeghem (UGent)
(2010) DESIGNS CODES AND CRYPTOGRAPHY. 55(2-3). p.121-130
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Abstract
In this note, we characterize the Grassmann embedding of H(q), q even, as the unique full embedding of H(q) in PG(12, q) for which each ideal line of H(q) is contained in a plane. In particular, we show that no such embedding exists for H(q), with q odd. As a corollary, we can classify all full polarized embeddings of H(q) in PG(12, q) with the property that the lines through any point are contained in a solid; they necessarily are Grassmann embeddings of H(q), with q even.
Keywords
Grassmann embedding, Generalized hexagon, Veronese surface, FINITE GENERALIZED HEXAGONS

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

Chicago
De Wispelaere, An, Joseph Thas, and Hendrik Van Maldeghem. 2010. “A Characterization of the Grassmann Embedding of H(q), with q Even.” Designs Codes and Cryptography 55 (2-3): 121–130.
APA
De Wispelaere, An, Thas, J., & Van Maldeghem, H. (2010). A characterization of the Grassmann embedding of H(q), with q even. DESIGNS CODES AND CRYPTOGRAPHY, 55(2-3), 121–130.
Vancouver
1.
De Wispelaere A, Thas J, Van Maldeghem H. A characterization of the Grassmann embedding of H(q), with q even. DESIGNS CODES AND CRYPTOGRAPHY. 2010;55(2-3):121–30.
MLA
De Wispelaere, An, Joseph Thas, and Hendrik Van Maldeghem. “A Characterization of the Grassmann Embedding of H(q), with q Even.” DESIGNS CODES AND CRYPTOGRAPHY 55.2-3 (2010): 121–130. Print.
@article{985002,
  abstract     = {In this note, we characterize the Grassmann embedding of H(q), q even, as the unique full embedding of H(q) in PG(12, q) for which each ideal line of H(q) is contained in a plane. In particular, we show that no such embedding exists for H(q), with q odd. As a corollary, we can classify all full polarized embeddings of H(q) in PG(12, q) with the property that the lines through any point are contained in a solid; they necessarily are Grassmann embeddings of H(q), with q even.},
  author       = {De Wispelaere, An and Thas, Joseph and Van Maldeghem, Hendrik},
  issn         = {0925-1022},
  journal      = {DESIGNS CODES AND CRYPTOGRAPHY},
  language     = {eng},
  number       = {2-3},
  pages        = {121--130},
  title        = {A characterization of the Grassmann embedding of H(q), with q even},
  url          = {http://dx.doi.org/10.1007/s10623-009-9336-5},
  volume       = {55},
  year         = {2010},
}

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