English

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

Combinatorics 2016-11-25 v1 Representation Theory

Abstract

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.

Keywords

Cite

@article{arxiv.1104.0324,
  title  = {On Binary Codes from Conics in PG(2,q)},
  author = {Adonus L. Madison and Junhua Wu},
  journal= {arXiv preprint arXiv:1104.0324},
  year   = {2016}
}
R2 v1 2026-06-21T17:48:36.219Z