论文标题
扩展的环状代码，最大弧和卵形
Extended cyclic codes, maximal arcs and ovoids
论文作者
论文摘要
我们表明，$ \ mathbb {f} _q $带有参数$ [q+2,3，q] $，$ q = 2^m $，确定常规hyperovals。我们还表明，具有参数的扩展循环代码$ [qt-q+t，3，qt-q] $，$ 1 <t <q $，确定（循环）Denniston Maximal Arcs。同样，具有参数的环状代码$ [q^2+1,4，q^2-q] $等效于$ pg（3，q）$中从椭圆四边形获得的卵形代码。最后，我们在$ pg（2，q）$和椭圆式四边形（3，q）$中提供了Denniston Maximal Arcs的新简单演示。
We show that extended cyclic codes over $\mathbb{F}_q$ with parameters $[q+2,3,q]$, $q=2^m$, determine regular hyperovals. We also show that extended cyclic codes with parameters $[qt-q+t,3,qt-q]$, $1<t<q$, determine (cyclic) Denniston maximal arcs. Similarly, cyclic codes with parameters $[q^2+1,4,q^2-q]$ are equivalent to ovoid codes obtained from elliptic quadrics in $PG(3,q)$. Finally, we give new simple presentations of Denniston maximal arcs in $PG(2,q)$ and elliptic quadrics in $PG(3,q)$.
