Designs, Codes and Cryptography

, Volume 68, Issue 1–3, pp 25–32 | Cite as

A small minimal blocking set in PG(n, p t ), spanning a (t − 1)-space, is linear



In this paper, we show that a small minimal blocking set with exponent e in PG(n, p t ), p prime, spanning a (t/e − 1)-dimensional space, is an \({\mathbb{F}_{p^e}}\) -linear set, provided that p > 5(t/e)−11. As a corollary, we get that all small minimal blocking sets in PG(n, p t ), p prime, p > 5t − 11, spanning a (t − 1)-dimensional space, are \({\mathbb{F}_p}\) -linear, hence confirming the linearity conjecture for blocking sets in this particular case.


Blocking set Linearity conjecture Linear set 

Mathematics Subject Classification (2010)



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© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Eötvös Loránd UniversityBudapestHungary
  2. 2.Vrije Universiteit BrusselBrusselBelgium

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