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

Sziklai, Péter and Van, De Voorde G (2013) A small minimal blocking set in PG(n, pt), spanning a (t − 1)-space, is linear. DESIGNS CODES AND CRYPTOGRAPHY, 68 (1-3). pp. 25-32. ISSN 0925-1022

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Abstract

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 Fp 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 F p -linear, hence confirming the linearity conjecture for blocking sets in this particular case. © 2012 Springer Science+Business Media New York.

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