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.
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Communicated by Ron Mullin, Rainer Steinwandt.
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De Wispelaere, A., Thas, J.A. & Van Maldeghem, H. A characterization of the Grassmann embedding of H(q), with q even. Des. Codes Cryptogr. 55, 121–130 (2010). https://doi.org/10.1007/s10623-009-9336-5
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DOI: https://doi.org/10.1007/s10623-009-9336-5