Graphical designs are an extension of spherical designs to functions on graphs. We connect linear codes to graphical designs on cube graphs, and show that the Hamming code in particular is a highly effective graphical design. We show that even in highly structured graphs, graphical designs are distinct from the related concepts of extremal designs, maximum stable sets in distance graphs, and $t$-designs on association schemes.
翻译：图形设计是图形中功能球形设计的延伸。 我们将线性代码与立方体图形中的图形设计连接起来, 并显示Hamming代码尤其是一个非常有效的图形设计。 我们显示,即使在高度结构化的图形中, 图形设计也与相关概念截然不同, 这些概念包括极端设计、 距离图中的最大稳定设置, 以及 $t$t-designs 组合方案。
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