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 \({\mathbb{F}_{p^e}}\) -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.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Finite Geometries”.
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Sziklai, P., Van de Voorde, G. A small minimal blocking set in PG(n, p t), spanning a (t − 1)-space, is linear. Des. Codes Cryptogr. 68, 25–32 (2013). https://doi.org/10.1007/s10623-012-9751-x
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DOI: https://doi.org/10.1007/s10623-012-9751-x