The coin weighing problem is the following: Given $n$ coins for which $m$ of them are counterfeit with the same weight. The problem is to detect the counterfeit coins with minimal number of weighings. This problem has many applications in compressed sensing, multiple access adder channels, etc. The problem was ... more >>>

We prove that for every prime $p$ there exists a $(0,1)$-matrix
$M$ of size $t_p(n,m)\times n$ where
$$t_p(n,m)=O\left(m+\frac{m\log \frac{n}{m}}{\log \min({m,p})}\right)$$ such that every
$m$ columns of $M$ are linearly independent over $\Z_p$, the field
of integers modulo $p$ (and therefore over any field of
characteristic $p$ and over the real ... more >>>