Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2021-02-01 , DOI: 10.1016/j.ffa.2021.101814 Nanami Bono , Tatsuya Maruta , Keisuke Shiromoto , Kohei Yamada
We prove that a non-trivial minimal blocking set with respect to hyperplanes in PG, , is a skeleton contained in some s-flat with odd . We also consider non-trivial minimal blocking sets with respect to lines and planes in PG, . Especially, we show that there are exactly two non-trivial minimal blocking sets with respect to lines and six non-trivial minimal blocking sets with respect to planes up to projective equivalence in PG. A characterization of an elliptic quadric in PG as a special non-trivial minimal blocking set with respect to planes meeting every hyperplane in a non-trivial minimal blocking sets with respect to planes is also given.
中文翻译:
关于二元射影空间中的非平凡最小阻塞集
我们证明了关于PG中超平面的非平凡最小阻塞集, 是一个包含在奇数个s平面中的骨架。我们还考虑了PG中关于线和平面的非平凡最小阻塞集, 。尤其是,我们表明在PG中,对于直线,正好有两个非平凡的最小阻塞集,而对于平面,正好有六个非平凡的最小阻塞集。PG中椭圆形二次曲面的刻画 因为还给出了相对于与满足平面的非平凡最小阻塞集合中的每个超平面有关的平面的特殊非平凡最小阻塞集合。