Secure Frameproof Code Through Biclique Cover
Hossein Hajiabolhassan, Farokhlagha Moazami

TL;DR
This paper establishes a connection between secure frameproof codes and biclique covers of Kneser graphs, providing new insights and bounds for their construction and properties.
Contribution
It characterizes the existence of secure frameproof codes via biclique covers of Kneser graphs and explores their relation to cover-free families, offering new bounds and theoretical insights.
Findings
Existence of secure frameproof codes characterized by 1-biclique covers of Kneser graphs.
Connection established between biclique covers and cover-free families.
An upper bound for the 1-biclique covering number of Kneser graphs provided.
Abstract
For a binary code of length , a -word produces by a set of codewords if for all , we have . We call a code -secure frameproof of size if and for any -word that is produced by two sets and of size at most then the intersection of these sets is nonempty. A -biclique cover of size of a graph is a collection of -complete bipartite subgraphs of such that each edge of belongs to at least of these complete bipartite subgraphs. In this paper, we show that for , an -secure frameproof code of size and length exists if and only if there exists a 1-biclique cover of size for the Kneser graph whose vertices are all -subsets of a -element set and two -subsets are adjacent if their intersection…
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · DNA and Biological Computing
