偏序集上的最优极小线性码
Optimal minimal Linear codes from posets
摘要：
最近，Hyun { \em et al}从单纯复形中构造了一些极小和最优二元线性码的无限族。我们将这种构造方法推广到任意偏序集。特别地，反链对应于单纯复形。本文给出了两种由两层递阶偏序集构造二元线性码的方法。特别地，我们确定了二元线性码的重量分布与层次偏序集的两个水平。在此基础上，我们还得到了一些不满足Ashikhmin-Barg条件的最优和最小二元线性码。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
