Weak arcs and applications to the DNA-based storage access problem

2026-08-19

AI Summary

研究弱弧及其在DNA存储访问问题中的应用，通过构造大平衡拟弧并给出弱弧的上界来解决随机访问问题。

Abstract

Weak arcs are point sets in PG$(n-1,q)$ meeting every general hyperplane (those are the hyperplanes not going through one of the points given by the standard basis vectors) in at most $n-1$ points. In this paper, we study weak arcs together with balanced variants which are contained on the sides of the fundamental simplex. We give an upper bound on the size of weak arcs, characterise the largest balanced quasi-arcs in the plane and construct large balanced quasi-arcs in PG$(3, q)$. We then use these configurations to build point sets for the random-access problem in DNA-based storage. The constructions are explicit, work over small fields, and attain recovery expectations matching the best known asymptotic bounds.

Problem

• weak arcs
• balanced variants
• DNA-based storage access problem

Innovation

• weak arcs
• balanced quasi-arcs
• DNA-based storage
• random-access problem
• small fields