几何差族与相关的变权重几何正交码
Geometric difference families and related variable-weight geometric orthogonal codes
- School of Mathematical Sciences, Hebei Normal University（河北师范大学数学科学学院）
- College of Basic Education, Beijing Institute of Economics and Management（北京经济管理职业学院基础教育部）
- Hebei Research Center of the Basic Discipline Pure Mathematics（河北省基础学科纯数学研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文基于几何差族与几何正交码的等价关系，证明了特定参数下GDFs的存在性，并完全确定了剩余参数，从而构造出三类完美变权重几何正交码。
AI中文摘要：
变权重几何正交码（GOCs）由Doty和Winslow引入，用于设计3D DNA折纸中的大分子键。最近，Wang等人引入了几何差族（GDFs）的概念，并建立了GOCs与某类GDFs之间的等价关系。基于该关系，Su等人给出了两类变权重GOCs。在本文中，我们首先证明了对于K={3,5}和{3,6}，存在(n*m,K,1)-GDFs。为了进一步研究，我们完全确定了Su等人提出的(n*m,{3,4,5},1)-GDF的所有剩余参数的存在的可能性。作为结果，我们获得了对于K={3,5}、{3,6}和{3,4,5}的完美(n*m,K,1)-GOCs。
英文摘要：
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.
