A proof of the linearity conjecture for k-blocking sets in PG(n, p3), p prime

Details A proof of the linearity conjecture for k-blocking sets in PG(n, p3), p prime A proof of the linearity conjecture for k-blocking sets in PG(n, p3), p prime

2012-01-16

arxiv.org/abs/1201.3296v1

J. Combin. Theory Ser. A 118 (2011), no. 3, 808--818

Mathematics

Combinatorics

Scientific paper

In this paper, we show that a small minimal k-blocking set in PG(n, q3), q =
p^h, h >= 1, p prime, p >=7, intersecting every (n-k)-space in 1 (mod q)
points, is linear. As a corollary, this result shows that all small minimal
k-blocking sets in PG(n, p^3), p prime, p >=7, are Fp-linear, proving the
linearity conjecture (see [7]) in the case PG(n, p3), p prime, p >= 7.

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