论文标题
极端类型II $ \ MATHBB {Z} _ {2K} $ - 代码的构建
Construction of extremal Type II $\mathbb{Z}_{2k}$-codes
论文作者
论文摘要
我们提供了构建许多自dual $ \ mathbb {z} _m $ -codes和类型II $ \ Mathbb {z} _ {2K} $ - 长度$ 2N $代码的方法$ 2N $。作为一个应用程序，我们构建了极端类型II $ \ MATHBB {Z} _ {2K} $ - 长度$ 24 $的代码$ k = 4,5，\ ldots，20 $和极端类型II $ \ MATHBB {Z} _ {2K} _ {2K} $ - 长度$ 32 $ for $ 32 $ for $ 32 $ $ 32 $ K = 4,5 $ \ ldots，\ ldots，10 $ ldots，10 $ ldots，10 $ ldots，\ ldots，10。我们还构建了新的极端类型II $ \ MATHBB {Z} _4 $ - 长度为$ 56 $和$ 64 $的代码。
We give methods for constructing many self-dual $\mathbb{Z}_m$-codes and Type II $\mathbb{Z}_{2k}$-codes of length $2n$ starting from a given self-dual $\mathbb{Z}_m$-code and Type II $\mathbb{Z}_{2k}$-code of length $2n$, respectively. As an application, we construct extremal Type II $\mathbb{Z}_{2k}$-codes of length $24$ for $k=4,5,\ldots,20$ and extremal Type II $\mathbb{Z}_{2k}$-codes of length $32$ for $k=4,5,\ldots,10$. We also construct new extremal Type II $\mathbb{Z}_4$-codes of lengths $56$ and $64$.
