Recently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun et al. We extend this construction method to arbitrary posets. Especially, anti-chains are corresponded to simplicial complexes. In this paper, we present two constructions of binary linear codes from hierarchical posets of two levels. In particular, we determine the weight distributions of binary linear codes associated with hierarchical posets with two levels. Based on these results, we also obtain some optimal and minimal binary linear codes not satisfying the condition of Ashikhmin–Barg.

中文翻译：

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来自posets的最优最小线性码

最近，Hyun 等人从单纯复形构造了一些无限族的最小和最优二进制线性码。我们将此构造方法扩展到任意偏序集。特别是，反链对应于简单的复合物。在本文中，我们提出了两种来自两级分层偏序集的二进制线性码的构造。特别是，我们确定了与具有两个级别的分层偏序集相关联的二进制线性代码的权重分布。基于这些结果，我们还获得了一些不满足 Ashikhmin-Barg 条件的最优和最小二进制线性代码。