Some new bounds for cover-free families

DOI10.1006/jcta.1999.3036zbMath0948.05055OpenAlexW2001779588MaRDI QIDQ1976329

Rui Zhong Wei, Lie Zhu, Douglas R. Stinson

Publication date: 9 May 2000

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcta.1999.3036

zbMATH Keywords

key distribution patternSperner's theoremcover-free familysuperimposed binary code

Mathematics Subject Classification ID

Extremal set theory (05D05) Combinatorial aspects of packing and covering (05B40)

Related Items (30)

Almost Optimal Cover-Free Families ⋮ A group testing method for finding patterns in data ⋮ Lower bounds for cover-free families ⋮ Exact learning from an honest teacher that answers membership queries ⋮ Generalised cumulative arrays in secret sharing ⋮ Secret sharing schemes with partial broadcast channels ⋮ Improved constructions for non-adaptive threshold group testing ⋮ Linear Time Constructions of Some $$d$$-Restriction Problems ⋮ Separating codes and a new combinatorial search model ⋮ Constructions for key distribution patterns ⋮ A survey on nonadaptive group testing algorithms through the angle of decoding ⋮ New combinatorial structures with applications to efficient group testing with inhibitors ⋮ Improved upper bounds for the rate of separating and completely separating codes ⋮ Unnamed Item ⋮ A note on the uniqueness of \((w, r)\) cover-free codes ⋮ Non-adaptive learning of a hidden hypergraph ⋮ Asymptotic bounds for the rate of colored superimposed codes ⋮ Smart elements in combinatorial group testing problems with more defectives ⋮ Generalized cover-free families. ⋮ An upper bound of the number of tests in pooling designs for the error-tolerant complex model ⋮ Transport schemes for topology-transparent scheduling ⋮ An unexpected meeting of four seemingly unrelated problems: graph testing, DNA complex screening, superimposed codes and secure key distribution ⋮ Threshold and Majority Group Testing ⋮ Group Testing with Multiple Mutually-Obscuring Positives ⋮ Some new bounds for cover-free families through biclique covers ⋮ Families of finite sets in which no intersection of \(\ell\) sets is covered by the union of \(s\) others ⋮ Bounds on the rate of disjunctive codes ⋮ A classification of the structures of some Sperner families and superimposed codes ⋮ Nonadaptive algorithms for threshold group testing ⋮ Non-adaptive Learning of a Hidden Hypergraph

Cites Work

• New combinatorial designs and their applications to group testing
• Families of finite sets in which no set is covered by the union of \(r\) others
• Key storage in secure networks
• Families of finite sets in which no set is covered by the union of two others
• On the upper bound of the size of the \(r\)-cover-free families
• Secure frameproof codes, key distribution patterns, group testing algorithms and related structures
• Bounds for key distribution patterns
• On key storage in secure networks
• On \(r\)-cover-free families
• Interval Packing and Covering in the Boolean Lattice
• Nonrandom binary superimposed codes
• Unnamed Item
• Unnamed Item

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