Abstract
In this note we use the spatial representation in \(\Sigma=PG(4,q)\) of the projective plane \(\Pi=PG(2,q^2)\), by fixing a hyperplane \(\Sigma'\) with a regular spread \(\mathcal S\) of lines. We consider a bundle \(\mathcal X\) of varieties \(V_2^3\) of \(\Sigma\) having in common the \(q+1\) points of a conic \(\mathcal C^2\) of a plane \(\pi_0\), \(\pi_0\cap \Sigma'=l_0\in \mathcal S\), thus representing an affine line of \(\Pi\), and a further affine point \(O\notin \pi_0\). This subset \(\mathcal X\) of \(\Sigma\) represents a bundle of non-affine Baer subplanes of \(\Pi\), each of them having one point at infinity (corresponding to a line of \(\mathcal S\)), having in common a subline of affine points of \(\Pi\) and a further affine point. Then \(\mathcal X\) is considered as a projective system of \(\Sigma\) and, by using such a representation of \(\Pi\), we can calculate the ground parameters of the code \(C_\mathcal X\) arising from it.
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