We examine the binary codes from adjacency matrices of the graph with vertices the nodes of the $ m $-ary $ n $-cube $ Q^m_n $ and with adjacency defined by the Lee metric. For $ n = 2 $ and $ m $ odd, we obtain the parameters of the code and its dual, and show the codes to be $ LCD $. We also find $ s $-PD-sets of size $ s+1 $ for $ s < \frac{m-1}{2} $ for the dual codes, i.e. $ [m^2,2m-1,m]_2 $ codes, when $ n = 2 $ and $ m\ge 5 $ is odd.

中文翻译：

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来自的二进制代码 \ begin {document} $ m $ \ end {document}-ary \ begin {document} $ n $ \ end {document}-立方体 \ begin {document} $ Q ^ m_n $ \ end {document}

我们检查图的邻接矩阵的二进制代码，其中顶点为$ m $ -ary $ n $-cube $ Q ^ m_n $的节点，并且邻接关系由Lee度量定义。对于$ n = 2 $和$ m $奇数，我们获得代码及其对偶的参数，并将代码显示为$ LCD $。我们还发现$ s $ -PD-sets大小为$ s + 1 $ for $ s <\ frac {m-1} {2} $为对偶代码，即$ [m ^ 2,2m-1，m] _2 $代码，当$ n = 2 $并且$ m \ ge 5 $是奇数时。