Abstract
A pseudo-embedding of a point-line geometry is a representation of the geometry into a projective space over the field \({\mathbb F}_2\) such that every line corresponds to a frame of a subspace. Such a representation is called homogeneous if every automorphism of the geometry lifts to an automorphism of the projective space. In this paper, we determine all homogeneous pseudo-embeddings of the three Witt designs that arise by extending the projective plane \({\mathrm{PG}}(2,4)\). Along our way, we come across some codes with automorphism group \(P\Sigma L(3,4)\) and sets of points of \({\mathrm{PG}}(2,4)\) that have a particular intersection pattern with Baer subplanes or hyperovals.
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The author Mou Gao, is supported by the State Scholarship Fund (File No. 201806065052) and the National Natural Science Foundation of China (Grant No. 71771035).
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De Bruyn, B., Gao, M. On four codes with automorphism group \(P\Sigma L(3,4)\) and pseudo-embeddings of the large Witt designs. Des. Codes Cryptogr. 88, 429–452 (2020). https://doi.org/10.1007/s10623-019-00690-1
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DOI: https://doi.org/10.1007/s10623-019-00690-1