<p style='text-indent:20px;'>In this paper we consider two pointsets in <inline-formula><tex-math>\begin{document}$ \mathrm{PG}(2,q^n) $\end{document}</tex-math></inline-formula> arising from a linear set <inline-formula><tex-math>\begin{document}$ L $\end{document}</tex-math></inline-formula> of rank <inline-formula><tex-math>\begin{document}$ n $\end{document}</tex-math></inline-formula> contained in a line of <inline-formula><tex-math>\begin{document}$ \mathrm{PG}(2,q^n) $\end{document}</tex-math></inline-formula>: the first one is a linear blocking set of Rédei type, the second one extends the construction of translation KM-arcs. We point out that their intersections pattern with lines is related to the weight distribution of the considered linear set <inline-formula><tex-math>\begin{document}$ L $\end{document}</tex-math></inline-formula>. We then consider the Hamming metric codes associated with both these constructions, for which we can completely describe their weight distributions. By choosing <inline-formula><tex-math>\begin{document}$ L $\end{document}</tex-math></inline-formula> to be an <inline-formula><tex-math>\begin{document}$ {\mathbb F}_{q} $\end{document}</tex-math></inline-formula>-linear set with a <i>short</i> weight distribution, then the associated codes have <i>few weights</i>. We conclude the paper by providing a connection between the <inline-formula><tex-math>\begin{document}$ \Gamma\mathrm{L} $\end{document}</tex-math></inline-formula>-class of <inline-formula><tex-math>\begin{document}$ L $\end{document}</tex-math></inline-formula> and the number of inequivalent codes we can construct starting from it.</p>

中文翻译：

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$ \mathrm{PG}(2,q^n) $ 中的两个点集和相关代码

我们指出，它们与线的交叉模式与所考虑的线性集合的权重分布有关 <inline-formula><tex-math>\begin{document}$ L $\end{document}</tex-math>< /内联公式>。然后我们考虑与这两种结构相关的汉明度量代码，我们可以完全描述它们的权重分布。通过选择 <inline-formula><tex-math>\begin{document}$ L $\end{document}</tex-math></inline-formula> 成为 <inline-formula><tex-math> \begin{document}$ {\mathbb F}_{q} $\end{document}</tex-math></inline-formula>-具有 <i>short</i> 权重分布的线性集，然后相关代码的权重<i>很少</i>。我们通过提供 <