Partial covers of PG(n, q)

In this paper, we investigate some properties of partial covers of PG(n, q). We show that a set of q + a hyperplanes, q 81, a < (q - 1)/3, or q > 13 and a (q - 10)/4, that does not cover PG(n, q), does not cover at least qn-1 - aqn-2 points, and that this bound is sharp. In the planar case, we show that if there are at most q + a non-covered points, q 81, a < (q - 1)/3, the non-covered points are collinear. In this case, the bound on a is sharp. Moreover, for PG(n, q), we show that for q 81 and a < (q - 1)/3, or q > 13 and a (q - 10)/4, if the number of non-covered points is at most qn-1 , then all non-covered points are contained in one hyperplane.

• Type: Journal
• Year: 2010
• Where: EJC
• Authors: Stefan M. Dodunekov, Leo Storme, Geertrui Van de Voorde
• Keywords: EJC 2007, EJC 2010, Hyperplane, Non-covered Points, Partial Covers