Blocking Sets and Derivable Partial Spreads
G. Lunardon
and O. Polverino
DOI: 10.1023/A:1011265919847
Abstract
We prove that a GF( q)-linear Rédei blocking set of size q t + q t-1 + ;;; + q + 1 of PG(2, q t) defines a derivable partial spread of PG(2 t - 1, q). Using such a relationship, we are able to prove that there are at least two inequivalent Rédei minimal blocking sets of size q t + q t-1 + ;;; + q + 1 in PG(2, q t), if t 
4.
4.Pages: 49–56
Keywords: spread; translation plane; blocking set
Full Text: PDF
References
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2. A.E. Brouwer and H.A. Wilbrink, “Blocking sets in translation planes,” J. Geom. 19 (1982), 200.
3. A. Bruen, “Blocking sets in finite projective planes,” Siam J. Appl. Math. 21 (3) (1971), 380-392.
4. A. Bruen, “Partial spreads and replaceable nets,” Can. J. Math. XX (3) (1971), 381-391.
5. P. Dembowski, Finite Geometries, Springer-Verlag, Berlin, 1968.
6. H. L\ddot uneburg, Translation Planes, Springer-Verlag, Berlin, 1980.
7. G. Lunardon, “Normal spreads,” Geom. Dedicata 75 (1999), 245-261.
8. G. Lunardon, “Linear k-blocking sets,” Combinatorica, to appear.
9. G. Lunardon, P. Polito, and O. Polverino, “A geometric characterisation of linear k-blocking sets,” J. Geom., to appear.
10. P. Polito and O. Polverino, “Blocking sets in André planes,” Geom. Dedicata 75 (1999), 199-207.
11. T.G. Ostrom, “Replaceable nets, net collineations, and net extensions,” Can. J. Math. 18 (1966), 666-672.
12. T. Sz\ddot onyi, “Blocking sets in desarguesian affine and projective planes,” Finite Fields Appl. 3 (1997), 187-202.