论文标题
POSET的最佳最小线性代码
Optimal minimal Linear codes from posets
论文作者
论文摘要
最近，一些最小和最佳二进制线性代码的无限族是由Hyun {\ em等人}构建的，我们将这种构造方法扩展到任意POSET。特别是，抗链对应于简单复合物。 在本文中，我们介绍了两个级别的分层posets的二进制线性代码的两个结构。特别是，我们确定与两个级别的分层poset相关的二进制线性代码的重量分布。基于这些结果，我们还获得了一些最佳和最小的二进制线性代码，无法满足Ashikhmin-Barg的状况。
Recently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun {\em 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.
