  This paper studies the random walk on the hypercube
$(\mathbb{Z}/2\mathbb{Z})^n$ which at each step flips $k$ randomly chosen
coordinates. We prove that the mixing time for this walk is of order
$\frac{n}{k} \log n$. We also prove that if $k=o(n)$, then the walk exhibits
cutoff at $\frac{n}{2k} \log n$ with window $\frac{n}{2k} $.
