论文标题
在$（q + 1）$ - 弧的几何形状上，$ \ mathrm {pg}（3，q）$，甚至
On the geometry of a $(q + 1)$-arc of $\mathrm{PG}(3, q)$, q even
论文作者
论文摘要
在$ \ mathrm {pg}（3，q）$中，$ q = 2^n $，$ n \ ge 3 $，让$ {\ cal a} = \ {（1，t，t，t，t，t，t^{2^h}，t^{2^{2^h+1}） \ {（0,0,0,1）\} $，带有$ \ mathrm {gcd}（n，h）= 1 $，为$（q+1）$ - arc，让$ g_h \ simeq \ simeq \ simeq \ mathrm {pgl}（pgl}（2，q）$是$ \ cal a $ in $ in $ in $ in的稳定性。 $ G_H $ -ORBITS在$ \ Mathrm {pg}（3，q）$的点，线和飞机上，以及相对于$ g_h $ -orbits的点平面入射矩阵，确定了$ G_H $ -ORBITS的点和飞机的$ \ MATHRM {pg}（pg}（3，q）$。还考虑了相对于$ g_1 $ -orbit的点线入射率矩阵的点和$ \ mathrm {pg}（3，q）$的行。特别是，对于属于给定行的$ g_1 $ -orbits的行$ \ ell $，例如$ \ cal l $，明确计算了$ \ ell $的点$ g_1 $ -orbit分布，或者证明它取决于$ x $ in $ \ nath $ \ nathbb {f} $ quand $ x $ _q $ _q $（或IN nath s sef） $ \ mathrm {tr} _ {q | 2}（g（x））= 0 $，其中$ g $是$ \ mathbb {f} _q $ -map由$ \ cal l $确定。
In $\mathrm{PG}(3, q)$, $q = 2^n$, $n \ge 3$, let ${\cal A} = \{(1,t,t^{2^h},t^{2^h+1}) \mid t \in \mathbb{F}_q\} \cup \{(0,0,0,1)\}$, with $\mathrm{gcd}(n,h) = 1$, be a $(q+1)$-arc and let $G_h \simeq \mathrm{PGL}(2, q)$ be the stabilizer of $\cal A$ in $\mathrm{PGL}(4, q)$. The $G_h$-orbits on points, lines and planes of $\mathrm{PG}(3, q)$, together with the point-plane incidence matrix with respect to the $G_h$-orbits on points and planes of $\mathrm{PG}(3, q)$ are determined. The point-line incidence matrix with respect to the $G_1$-orbits on points and lines of $\mathrm{PG}(3, q)$ is also considered. In particular, for a line $\ell$ belonging to a given line $G_1$-orbits, say $\cal L$, the point $G_1$-orbit distribution of $\ell$ is either explicitly computed or it is shown to depend on the number of elements $x$ in $\mathbb{F}_q$ (or in a subset of $\mathbb{F}_q$) such that $\mathrm{Tr}_{q|2}(g(x)) = 0$, where $g$ is an $\mathbb{F}_q$-map determined by $\cal L$.
