English

Quantitative Frameproof Codes and Hypergraphs

Combinatorics 2025-11-25 v1

Abstract

Frameproof codes are a class of secure codes introduced by Boneh and Shaw in the context of digital fingerprinting, and have been widely studied from a combinatorial point of view. In this paper, we study a quantitative extension of frameproof codes and hypergraphs, referred to as {\it quantitative frameproof codes and hypergraphs}. We give asymptotically optimal bounds on the maximum sizes of these structures and determine their exact sizes for a broad range of parameters. In particular, we introduce a generalized version of the Erd\H{o}s matching number in our proof and derive relevant estimates for it.

Keywords

Cite

@article{arxiv.2511.17912,
  title  = {Quantitative Frameproof Codes and Hypergraphs},
  author = {Wenjie Zhong and Xinqi Huang and Xiande Zhang},
  journal= {arXiv preprint arXiv:2511.17912},
  year   = {2025}
}