TY - JOUR
T1 - Union–intersection-bounded families and their applications
AU - Gu, Y.
AU - Miao, Ying
N1 - Funding Information:
Research supported by JSPS Grant-in-Aid for Scientific Research (B) under Grant No. 18H01133. The authors express their gratitude to A. G. D'yachkov for providing Reference [4], and to the two anonymous reviewers for their detailed and constructive comments which are very useful to the improvement of the presentation of this paper.
Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2019/8/15
Y1 - 2019/8/15
N2 - 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).
AB - 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).
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U2 - 10.1016/j.dam.2018.12.002
DO - 10.1016/j.dam.2018.12.002
M3 - Article
AN - SCOPUS:85058821969
SN - 0166-218X
VL - 266
SP - 346
EP - 354
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -