Designs and their codes
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
On binary codes from conics in PG(2,q)
European Journal of Combinatorics
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Let $${\mathcal{L}}$$ and $${\mathcal{L}_0}$$ be the binary codes generated by the column $${\mathbb{F}_2}$$-null spaces of the incidence matrices of external points versus passant lines and internal points versus secant lines with respect to a conic in PG(2, q), respectively. We confirm the conjectures on the dimensions of $${\mathcal{L}}$$ and $${\mathcal{L}_0}$$ using methods from both finite geometry and modular representation theory.