Union–intersection-bounded families and their applications

Y. Gu*, Ying Miao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Cover-free families have been widely studied over recent decades due to their applications in numerous subjects. In this paper, we introduce the concept of (s,t;d)-union–intersection-bounded families, which is a generalization of t-cover-free families. We provide a general upper bound on the maximum size of an (s,t;d)-union–intersection-bounded family, and show a probabilistic lower bound for the case that the ground set is sufficiently large. They have the same order of magnitude for certain cases. We also discuss the applications of (s,t;d)-union–intersection-bounded families in broadcast encryption, and derive a better upper bound for (1,t;d)-union–intersection-bounded families (also known as superimposed distance codes).

Original languageEnglish
Pages (from-to)346-354
Number of pages9
JournalDiscrete Applied Mathematics
StatePublished - 15 Aug 2019
Externally publishedYes


  • Broadcast encryption
  • Cover-free family
  • Superimposed distance code
  • Union–intersection-bounded family


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