کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4653905 | 1632800 | 2012 | 16 صفحه PDF | دانلود رایگان |
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 qq is an odd prime power. In this article, we study both geometric and algebraic properties of the column F2F2-null space LL of A. In particular, using methods from both finite geometry and modular presentation theory, we manage to compute the dimension of LL, which provides a proof for the conjecture on the dimension of the binary code generated by LL.
► We study algebraic and geometric properties of conics in PG(2,q).
► We confirm the conjecture on the dimension of the F2F2-null space of the incidence matrix of passant lines and internal points.
► The tools involved are some results on modular representations of PSL(2,q).
Journal: European Journal of Combinatorics - Volume 33, Issue 1, January 2012, Pages 33–48