Optimal minimal Linear codes from posets
Information Theory
2020-08-18 v1 Combinatorics
math.IT
Abstract
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.
Keywords
Cite
@article{arxiv.2008.07212,
title = {Optimal minimal Linear codes from posets},
author = {Jong Yoon Hyun and Hyun Kwang Kim and Yansheng Wu and Qin Yue},
journal= {arXiv preprint arXiv:2008.07212},
year = {2020}
}
Comments
22 pages, to appear in DCC