Journal ArticleDOI
On blocking sets of quadrics
TLDR
In this article, the smallest blocking sets with respect to higher dimensional subspaces in the quadrics Q(2n, q) and Q+(2n+ 1, q).Abstract:
We determine the three smallest blocking sets with respect to lines of the quadric Q(2n, q) withn ≥ 3 and the two smallest blocking sets with respect to lines of the quadric Q+(2n+1,q) withn ≥ 2. These results will be used in a forthcoming paper for determining the smallest blocking sets with respect to higher dimensional subspaces in the quadrics Q(2n, q) and Q+(2n+ 1, q).read more
Citations
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Journal ArticleDOI
On codewords in the dual code of classical generalised quadrangles and classical polar spaces
TL;DR: It is shown that there exists an interval such that for every even number w in this interval, there is a codeword in the dual code of Q^+(5,q), q even, with weight w and there is an empty interval in the weight distribution of the dual of the code ofQ(4,q, q even).
Journal ArticleDOI
Small point sets that meet all generators of Q (2 n,p ), p >3 prime
Jan De Beule,Klaus Metsch +1 more
TL;DR: It is shown that the smallest cardinality of a set of points of Q(6, q), q > 3, q a prime has no ovoids, and this result is generalized to Q(2n, q).
Journal ArticleDOI
A Bose‐Burton type theorem for quadrics
TL;DR: The smallest cardinality of a set of points with the property that every subspace of dimension k that is contained in a non-degenerate quadric defined by a quadratic form in the finite projective space PG(d,q) is known.
Journal ArticleDOI
Bose-Burton type theorems for finite Grassmannians
TL;DR: In this paper both blocking sets with respect to the s- subspaces and covers with t-subspaces in a finite Grassmannian are investigated, especially focusing on geometric descriptions of blocking sets and covers of minimum size.
References
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Book
Projective geometries over finite fields
TL;DR: The first properties of the plane can be found in this article, where the authors define the following properties: 1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. Ovals 9. Arithmetic of arcs of degree two 10. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes 15.
BookDOI
General Galois geometries
TL;DR: In this paper, the authors define Hermitian varieties, Grassmann varieties, Veronese and Segre varieties, and embedded geometries for finite projective spaces of three dimensions.
Journal ArticleDOI
Baer subplanes and blocking sets
TL;DR: In this article, it was shown that a blocking set S in a projective plane w is a subset of the points of 7T such that every line of ir contains at least one point of 5 and at least another point which is not in S. Denoting the number of points in S by w, the main result, obtained by purely combinatorial means, is the following: if ir is finite of square order, say m, then | S| ^ m 2 + m + 1 and if | S\\ = ra+m + l, then the points
Journal ArticleDOI
Some p -Ranks Related to Orthogonal Spaces
Aart Blokhuis,G. Eric Moorhouse +1 more
TL;DR: In this paper, the p-rank of the incidence matrix of hyperplanes of PG(n, pe) and points of a non-degenerate quadric is determined, which yields new bounds for ovoids and the size of caps in finite orthogonal spaces.
Blocking sets in Desarguesian planes
TL;DR: In this paper, the authors survey recent results concerning the size of blocking sets in desarguesian projective and affine planes, and the implications of these results and the technique to prove them.
Related Papers (5)
On Blocking Sets of External Lines to a Hyperbolic Quadric in PG(3, q), q Even
Paola Biondi,Pia Maria Lo Re +1 more