论文标题
有关某些二进制代码的Assmus-Mattson定理的注释
A note on the Assmus--Mattson theorem for some binary codes
论文作者
论文摘要
我们以前提出了代码的第一个非平凡示例，该代码对从Assmus-Mattson定理获得的所有权重支持$ t $ designs，并具有支持$ t'$ - 具有一些$ t'> t $的$ t'$ - 设计。这表明了概括Assmus-Mattson定理的可能性，这在设计和编码理论中非常重要。在本文中，我们将这个示例概括为沿该方向的Assmus-Mattson定理的加强。作为推论，我们提供了扩展的Golay代码$ \ MATHCAL {G} _ {24} $的新特征。
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 $\mathcal{G}_{24}$.
