On Binary Codes from Conics in PG(2,q)

Details On Binary Codes from Conics in PG(2,q) On Binary Codes from Conics in PG(2,q)

2011-04-02

arxiv.org/abs/1104.0324v1

Mathematics

Combinatorics

Scientific paper

Let A be the 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 null space L of A over the finite field of 2 elements. 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.

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