论文标题
关于Assmus的注释 - 马特森类型定理
A note on Assmus--Mattson type theorems
论文作者
论文摘要
在本文中，我们为代码和晶格提供了Assmus-Mattson类型定理。我们表明，最小重量为24m的长度为24m的二进制双二进制代码提供了一个组合1设计，甚至具有最低标准2M 24m等级的单型晶格，提供了一个球形的3设计。我们指出，一些此类代码和晶格为T-Designs提供了更高t的t-designs。作为推论，我们对二进制的重量列出了二进制的重量，即使是长度为24m，重量为4M的自偶联代码。还给出了三元和第四纪类似物。
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 24m with minimum weight 4m provides a combinatorial 1-design and an even unimodular lattice of rank 24m with minimum norm 2m provides a spherical 3-design. We remark that some of such codes and lattices give t-designs for higher t. As a corollary, we give some restrictions on the weight enumerators of binary doubly even self-dual codes of length 24m with minimum weight 4m. Ternary and quaternary analogues are also given.
