Let $\mathrm{PG}(3,q)$ be the projective space of dimension three over the finite field with q elements. Consider a twisted cubic in $\mathrm{PG}(3,q)$. The structure of the point-plane incidence matrix in $\mathrm{PG}(3,q)$ with respect to the orbits of points and planes under the action of the stabilizer group of the twisted cubic is described. This information is used to view generalized doubly-extended Reed-Solomon codes of codimension four as asymptotically optimal multiple covering codes.

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在平面上通过PG（3，q）中的扭曲立方的点以及多个覆盖代码

让 $\mathrm{PG}（3，q）$是具有q个元素的有限域上第3维的投影空间。考虑一个扭曲的立方英寸$\mathrm{PG}（3，q）$。点平面入射矩阵的结构$\mathrm{PG}（3，q）$描述了在扭曲三次方的稳定器群的作用下关于点和平面的轨道。此信息用于查看四维渐近最优多重覆盖码的广义双扩展Reed-Solomon码。