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(2016)JOURNAL OF COMBINATORIAL DESIGNS.24(1).p.36-52 Mark abstract We present a construction for minimal blocking sets with respect to (k-1)-spaces in PG (n-1,qt), the (n-1)-dimensional projective space over the finite field Fqt of order qt. The construction relies on the use of blocking cones in the field reduced representation of PG (n-1,qt), extending the well-known construction of linear blocking sets. This construction is inspired by the construction for minimal blocking sets with respect to the hyperplanes by Mazzocca, Polverino, and Storme (the MPS-construction); we show that for a suitable choice of the blocking cone over a planar blocking set, we obtain larger blocking sets than the ones obtained from planar blocking sets in F. Mazzocca and O. Polverino, J Algebraic Combin 24(1) (2006), 61-81. Furthermore, we show that every minimal blocking set with respect to the hyperplanes in PG (n-1,qt) can be obtained by applying field reduction to a minimal blocking set with respect to (nt-t-1)-spaces in PG (nt-1,q). We end by relating these constructions to the linearity conjecture for small minimal blocking sets. We show that if a small minimal blocking set is constructed from the MPS-constructionthen it is of Redei-type, whereas a small minimal blocking set arises from our cone construction if and only if it is linear.

Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-7053582



Author: Geertrui Van de Voorde

Source: https://biblio.ugent.be/publication/7053582



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