Characterization results on small blocking sets of the polar spaces Q +(2n + 1, 2) and Q +(2n + 1, 3)

In De Beule and Storme, Des Codes Cryptogr 39(3):323–333, De Beule and Storme characterized the smallest blocking sets of the hyperbolic quadrics Q ⁺(2n + 1, 3), n ≥ 4; they proved that these blocking sets are truncated cones over the unique ovoid of Q ⁺(7, 3). We continue this research by classifying all the minimal blocking sets of the hyperbolic quadrics Q ⁺(2n + 1, 3), n ≥ 3, of size at most 3 ⁿ + 3 ^n–2. This means that the three smallest minimal blocking sets of Q ⁺(2n + 1, 3), n ≥ 3, are now classified. We present similar results for q = 2 by classifying the minimal blocking sets of Q ⁺(2n + 1, 2), n ≥ 3, of size at most 2 ⁿ + 2 ^n-2. This means that the two smallest minimal blocking sets of Q ⁺(2n + 1, 2), n ≥ 3, are classified.