LDPC codes generated by conics in the classical projective plane
Designs, Codes and Cryptography
Dimensions of some binary codes arising from a conic in PG(2,q)
Journal of Combinatorial Theory Series A
Proofs of two conjectures on the dimensions of binary codes
Designs, Codes and Cryptography
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Let A be the q(q-1)2xq(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 F"2-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.