Conics arising from internal points and their binary codes

In this article, with respect to a fixed conic, we construct conics only consisting of internal points. We first study the intersection pattern of each of these conics with passant lines and then compute the dimension of the F2-row space of the incidence matrix of the aforementioned conics and internal points. As a result, we obtain the dimension of the binary code constructed from the F2-null space of the above incidence matrix.