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arXiv · 2511.17912

Quantitative Frameproof Codes and Hypergraphs

Wenjie Zhong·Xinqi Huang·Xiande Zhang
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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.

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Wenjie Zhong, Xinqi Huang, Xiande Zhang. 2025-11-22. Quantitative Frameproof Codes and Hypergraphs. https://arxiv.org/abs/2511.17912

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