Work

Geometric difference families and related variable-weight geometric orthogonal codes

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.29202

Authors: Gao, Huizhen, Bai, Yichen, Su, Xiaowei, Tian, Zihong

Institutions: Hebei Normal University, Beijing Institute of Economics and Management

Language: English

Topic: Coding theory and cryptography

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Hebei Normal University, Natural Science Foundation of Hebei Province, Division of Mathematical Sciences

Awards: G6559391137, G763585163, G7672064112