2020/08/17 by Jong Yoon Hyun, Hyun, Jong Yoon, Hyun Kwang Kim +5 · 3 citations
Computer Science · Engineering · Medicine · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Multiple Myeloma Research and Treatments #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2008.07212
openalex publication_date 2020/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.