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On Blocking Sets in Affine Hjelmslev Planes

Boev, Stoyan, Landjev, Ivan (2012)

Serdica Journal of Computing

ACM Computing Classification System (1998): G.2.1.We prove that the minimum size of an affine blocking set in the affine plane AHG ...This research has been supported by the Scientific Research Fund of Sofia University under Contract No 109/09.05.2012.

On Cameron-Liebler line classes.

Govaerts, Patrick, Storme, Leo (2004)

Advances in Geometry

On Mathon's construction of maximal arcs in Desarguesian planes.

Fiedler, F., Leung, Ka Hin, Xiang, Qing (2003)

Advances in Geometry

On minimum size blocking sets of external lines to a quadric in $PG (3, q)$ .

Biondi, P., Lo Re, P.M.L., Storme, L. (2007)

Beiträge zur Algebra und Geometrie

On multiple nuclei and a conjecture of Lunelli and Sce.

Blokhuis, A. (1994)

Bulletin of the Belgian Mathematical Society - Simon Stevin

On sets of vectors of a finite vector space in which every subset of basis size is a basis

Simeon Ball (2012)

Journal of the European Mathematical Society

It is shown that the maximum size of a set $S$ of vectors of a $k$ -dimensional vector space over $𝔽_{q}$ , with the property that every subset of size $k$ is a basis, is at most $q + 1$ , if $k \leq p$ , and at most $q + k - p$ , if $q \geq k \geq p + 1 \geq 4$ , where $q = p^{k}$ and $p$ is prime. Moreover, for $k \leq p$ , the sets $S$ of maximum size are classified, generalising Beniamino Segre’s “arc is a conic” theorem. These results have various implications. One such implication is that a $k \times (p + 2)$ matrix, with $k \leq p$ and entries from $𝔽_{p}$ , has $k$ columns which are linearly dependent. Another is...

Displaying 1 – 10 of 10

On Blocking Sets in Affine Hjelmslev Planes

On Cameron-Liebler line classes.

On Mathon's construction of maximal arcs in Desarguesian planes.

On minimum size blocking sets of external lines to a quadric in $PG (3, q)$ .

On multiple nuclei and a conjecture of Lunelli and Sce.

On sets of vectors of a finite vector space in which every subset of basis size is a basis

On some properties of a class of geometrical figures.

On the linearity of higher-dimensional blocking sets.

On the non-existence of certain hyperovals in dual André planes of order 2 $^{2 h}$ .

On the size of maximal caps in $Q^{+} (5, q)$ .

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