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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
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DTSTART:20250101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260428T163000
DTEND;TZID=Asia/Seoul:20260428T173000
DTSTAMP:20260415T182400
CREATED:20260303T004153Z
LAST-MODIFIED:20260303T004338Z
UID:12388-1777393800-1777397400@dimag.ibs.re.kr
SUMMARY:Xin Wei\, Separating hash families with large universe
DESCRIPTION:Separating hash families are useful combinatorial structures that generalize several well-studied objects in cryptography and coding theory. Let $p_t(N\, q)$ denote the maximum size of the universe for a $t$-perfect hash family of length $N$ over an alphabet of size $q$. We show that $q^{2 – o(1)} < p_t(t\, q) = o(q^2)$ for all  $t \ge 3$\, thereby resolving an open problem raised by Blackburn et al. (2008) for certain parameter ranges. Previously\, this result was known only for $t = 3$ and $t = 4$. Our approach establishes the existence of a large set of integers that avoids nontrivial solutions to a system of correlated linear equations. This is joint work with Xiande Zhang and Gennian Ge.
URL:https://dimag.ibs.re.kr/event/2026-04-28/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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