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 $\mathcal{G}_{24}$.

翻译：我们先前曾提出第一个非三重例子,说明一项守则支持从Assmus-Mattson定理中获得的所有重量设计值的美元设计值,并且支持一些重量设计值的美元设计值,加上一些美元。这表明有可能推广Assmus-Mattson定理,这对于设计和编码理论非常重要。在本文件中,我们把这个例子概括为沿着这个方向加强Asssmus-Mattson定理。作为必然结果,我们提供了对扩展的Golay 代码的新的定性 $\ mathcal{G ⁇ 24}$。