Geometric difference families and related variable-weight geometric orthogonal codes
Huizhen Gao, Yichen Bai, Xiaowei Su, Zihong Tian
Source abstract
Variable-weight geometric orthogonal codes (GOCs) were introduced by Doty and Winslow for designing the macrobonds in 3D DNA origami. Recently, Wang et al. introduced the concept of geometric difference families (GDFs) and established the equivalence between GOCs and a certain type of GDFs. Based on the relationship, Su et al. gave two classes of variable-weight GOCs. In this paper, we first prove the existence of (n*m,K,1)-GDFs for K ={3,5} and {3,6}. For further research, we completely determine the existence of all the remaining parameters for an (n*m,{3,4,5},1)-GDF by Su et al. As consequences, the perfect (n*m,K,1)-GOCs for K = {3,5}, {3,6} and {3,4,5} are obtained.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.