- Series
- Joint School of Mathematics and ACO Colloquium
- Time
- Thursday, September 26, 2013 - 4:30pm for 1 hour (actually 50 minutes)
- Location
- Skyles 005
- Speaker
- Zoltan Furedi – Renyi Institute of Mathematics of the Hungarian Academy of Sciences
- Organizer
- Karim Lounici

**Please Note:** Refreshements served at 4:00pm

There are many instances in Coding Theory when codewords must be
restored from partial information, like defected data (error correcting
codes), or some superposition of the strings.These lead to superimposed
codes, close relatives of group testing problems.There are lots of
versions and related problems, likeSidon sets, sum-free sets, union-free
families, locally thin families, cover-free codes and families, etc.We
discuss two cases {\it cancellative} and {\it union-free} codes.A family
of sets $\mathcal F$ (and the corresponding code of0-1 vectors) is
called {\bf union-free} if $A\cup B = C\cup D$ and $A,B,C,D\in \mathcal
F$ imply $\{ A,B\}=\{ C, D \}$.$\mathcal F$ is called $t$-{\bf
cancellative}if for all distict $t+2$ members $A_1, \dots, A_t$ and
$B,C\in \mathcal F$ $$A_1\cup\dots \cup A_t\cup B \neq A_1\cup \dots
A_t \cup C. $$Let $c_t(n)$ be the size of the largest $t$-cancellative
code on $n$elements. We significantly improve the previous upper bounds
of Alon, Monti, K\"orner and Sinaimeri, and introduce a method to deal
with such problems, namely to investigate first the constant weight case
(i.e., uniform hypergraphs).