On binary codes from conics in PG(2,q)

摘要

Let A be the q(q-1)/2 × q(q-1)/2 incidence matrix of passant lines and internal points with respect to a conic in PG(2,q), where q is an odd prime power. In this article, we study both geometric and algebraic properties of the column F2-null space L of A. In particular, using methods from both finite geometry and modular presentation theory, we manage to compute the dimension of L, which provides a proof for the conjecture on the dimension of the binary code generated by L.