On four codes with automorphism group P Sigma L(3,4) and pseudo-embeddings of the large Witt designs

Abstract

A pseudo-embedding of a point-line geometry is a representation of the geometry into a projective space over the field 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 PG(2, 4). Along our way, we come across some codes with automorphism group P Sigma L(3, 4) and sets of points of PG(2, 4) that have a particular intersection pattern with Baer subplanes or hyperovals