论文标题
PG（1，Q^5）中线性集的重量分布
The weight distributions of linear sets in PG(1,q^5)
论文作者
论文摘要
在本文中，我们研究了$ \ mathbb {f} _q $ -linear set $ \ mathrm {pg}（1，q^5）$的权重分布。我们的主要定理证明，线性套装的排名$ 5 $，并非分散，其重量大于1：（i）一点点重量$ 4 $ $ 4 $或5 $，（ii）一点点重量$ 3 $和$ 3 $和$ 0 $，$ q $，$ q $，$ Q $，$ q^2 $ $ $ $ $ $ $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 [q-2 \ sqrt {q}+1，q+2 \ 2 \ sqrt {q} +1] \ cup \ {2q，2q+1,2q+2,3q，3q+1，q^2+1 \} $。特别是，$ \ mathrm {pg}（1，q^5）$中没有$ 2 $ -CLUBS。
In this paper, we study the weight distributions of $\mathbb{F}_q$-linear sets in $\mathrm{PG}(1,q^5)$. Our main theorem proves that a linear set $S$ of rank $5$, which is not scattered has the following weight distribution for its points with weight larger than 1: (i) one point of weight $4$ or $5$, (ii) one point of weight $3$ and $0$, $q$, $q^2$ points of weight two, (iii) $s$ points of weight $2$ where $s\in [q-2\sqrt{q}+1,q+2\sqrt{q}+1]\cup\{2q,2q+1,2q+2,3q,3q+1,q^2+1\}$. In particular, there are no $2$-clubs in $\mathrm{PG}(1,q^5)$.
