关于PG（2，q）中的超聚焦弧
On Hyperfocused Arcs in PG(2,q)
摘要：
迪尔格斯射影平面中的k弧，其割线与k-1个点中的某条外线相交，称为超聚焦。超聚焦弧调查与秘密共享方案的基础上几何由于西蒙斯。本文证明了点轨道在适当的扩张群下是超聚焦弧，具有既不包含在超椭圆中，也不包含在真子平面中的重要性质。此外，广义超聚焦弧的概念，即弧的割线允许一个最小尺寸的块集，被引入：提供一个构造方法，连同分类的大小为10。
英文摘要：
A k-arc in a Dearguesian projective plane whose secants meet some external line in k-1 points is said to be hyperfocused. Hyperfocused arcs are investigated in connection with a secret sharing scheme based on geometry due to Simmons. In this paper it is shown that point orbits under suitable groups of elations are hyperfocused arcs with the significant property of being contained neither in a hyperoval, nor in a proper subplane. Also, the concept of generalized hyperfocused arc, i.e. an arc whose secants admit a blocking set of minimum size, is introduced: a construction method is provided, together with the classification for size up to 10.
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