Multiple Blocking Sets in PG(n, q), n > 3 |
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Authors: | János Barát Leo Storme |
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Affiliation: | (1) Bolyai Institute, University of Szeged, Aradi Vértanúk tere 1., 6720, Hungary;(2) Department of Pure Maths and Computer Algebra, Ghent University, Krijgslaan 281, 9000 Ghent, Belgium |
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Abstract: | This article discusses minimal s-fold blocking sets B in PG (n, q), q = ph, p prime, q > 661, n > 3, of size |B| > sq + cpq2/3 - (s - 1) (s - 2)/2 (s > min (cpq1/6, q1/4/2)). It is shown that these s-fold blocking sets contain the disjoint union of a collection of s lines and/or Baer subplanes. To obtain these results, we extend results of Blokhuis–Storme–Szönyi on s-fold blocking sets in PG(2, q) to s-fold blocking sets having points to which a multiplicity is given. Then the results in PG(n, q), n 3, are obtained using projection arguments. The results of this article also improve results of Hamada and Helleseth on codes meeting the Griesmer bound. |
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Keywords: | multiple blocking sets Baer subplanes minihypers |
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