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. When such a description exists, it is called a Bose–Burton type theorem. The canonical example of a blocking set with respect to the s-subspaces is the intersection of s linear complexes. In some cases such an intersection is a blocking set of minimum size, that can occasionally be characterized by a Bose–Burton type theorem. In particular, this happens for the 1-blocking sets of the Grassmannian of planes of PG( 5 , q ) .

Bose-Burton type theorems for finite Grassmannians

ZANELLA, CORRADO
2009

Abstract

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. When such a description exists, it is called a Bose–Burton type theorem. The canonical example of a blocking set with respect to the s-subspaces is the intersection of s linear complexes. In some cases such an intersection is a blocking set of minimum size, that can occasionally be characterized by a Bose–Burton type theorem. In particular, this happens for the 1-blocking sets of the Grassmannian of planes of PG( 5 , q ) .
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2381802
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