Constructing minimal blocking sets using field reduction [article]

Geertrui Van de Voorde
2015 arXiv   pre-print
We present a construction for minimal blocking sets with respect to (k-1)-spaces in PG(n-1,q^t), the (n-1)-dimensional projective space over the finite field F_q^t of order q^t. The construction relies on the use of blocking cones in the field reduced representation of PG(n-1,q^t), extending the well-known construction of linear blocking sets. This construction is inspired by the construction for minimal blocking sets with respect to the hyperplanes by Mazzocca, Polverino and Storme ( the
more » ... nstruction); we show that for a suitable choice of the blocking cone over a planar blocking set, we obtain larger blocking sets than the ones obtained from planar blocking sets in pol. Furthermore we show that every minimal blocking set with respect to the hyperplanes in PGPG(n-1,q^t) can be obtained by applying field reduction to a minimal blocking set with respect to (nt-t-1)-spaces in PG(nt-1,q). We end by relating these constructions to the linearity conjecture for small minimal blocking sets. We show that if a small minimal blocking set is constructed from the MPS-construction, it is of Rédei-type whereas a small minimal blocking set arises from our cone construction if and only if it is linear.
arXiv:1512.04822v1 fatcat:xqdxixcdebgj3nocrgr2n3gyou