Abstract
In this article we study minimal1-blocking sets in finite projective spaces PG(n,q),n ≥ 3. We prove that in PG(n,q 2),q = p h, p prime, p > 3,h ≥ 1, the second smallest minimal 1-blockingsets are the second smallest minimal blocking sets, w.r.t.lines, in a plane of PG(n,q 2). We also study minimal1-blocking sets in PG(n,q 3), n ≥ 3, q = p h, p prime, p > 3,q ≠ 5, and prove that the minimal 1-blockingsets of cardinality at most q 3 + q 2 + q + 1 are eithera minimal blocking set in a plane or a subgeometry PG(3,q).
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Storme, L., Weiner, Z. On 1-Blocking Sets in PG(n,q), n ≥ 3. Designs, Codes and Cryptography 21, 235–251 (2000). https://doi.org/10.1023/A:1008308200010
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DOI: https://doi.org/10.1023/A:1008308200010