A note on Assmus-Mattson type theorems
A note on Assmus-Mattson type theorems
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关于 Assmus-Mattson 型定理的注释
DOI：
10.1007/s10623-021-00848-w
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Akihiro Munemasa & Hiroyuki Nakasora
中科院分区：
文献类型：
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作者：
Tsuyoshi Miezaki;Akihiro Munemasa & Hiroyuki Nakasora
本文给出了码和格的Assmus-Mattson型定理。证明了长度为24m的最小重量为4m的二元双偶自对偶码提供了一种组合1-设计，具有最小范数为2m的秩为24m的偶么模格提供了一种球形3-设计。我们注意到一些这样的码和格是为Highert设计的。作为推论，我们给出了长度为24m的最小重量为4m的二元双偶自对偶码的重量枚举数的一些限制。还给出了三元和四元类似物。
In the present paper, we give Assmus–Mattson type theorems for codes and lattices. We show that a binary doubly even self-dual code of length 24mwith minimum weight 4mprovides a combinatorial 1-design and an even unimodular lattice of rank 24mwith minimum norm 2mprovides a spherical 3-design. We remark that some of such codes and lattices givet-designs for highert. As a corollary, we give some restrictions on the weight enumerators of binary doubly even self-dual codes of length 24mwith minimum weight 4m. Ternary and quaternary analogues are also given.