We previously proposed the first nontrivial examples of a code having support t-designs for all weights obtained from the Assmus-Mattson theorem and having support t'-designs for some weights with some t'>t. This suggests the possibility of generalizing the Assmus-Mattson theorem, which is very important in design and coding theory. In the present paper, we generalize this example as a strengthening of the Assmus-Mattson theorem along this direction. As a corollary, we provide a new characterization of the extended Golay code G_24.

中文翻译：

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加强 Assmus--Mattson 定理对一些对偶码

我们之前提出了代码的第一个非平凡示例，该代码支持从 Assmus-Mattson 定理获得的所有权重的 t-designs，并且支持某些 t'>t 的权重的 t'-designs。这表明可以推广 Assmus-Mattson 定理，这在设计和编码理论中非常重要。在本文中，我们将这个例子概括为沿这个方向加强 Assmus-Mattson 定理。作为推论，我们提供了扩展 Golay 代码 G_24 的新特征。