  The $i$th coordinate of an $(n,k)$ code is said to have locality $r$ and
availability $t$ if there exist $t$ disjoint groups, each containing at most
$r$ other coordinates that can together recover the value of the $i$th
coordinate. This property is particularly useful for codes for distributed
storage systems because it permits local repair and parallel accesses of hot
data. In this paper, for any positive integers $r$ and $t$, we construct a
binary linear code of length $\binom{r+t}{t}$ which has locality $r$ and
availability $t$ for all coordinates. The information rate of this code attains
$\frac{r}{r+t}$, which is always higher than that of the direct product code,
the only known construction that can achieve arbitrary locality and
availability.
