We design the first efficient algorithms and prove new combinatorial bounds for list decoding tensor products of codes and interleaved codes.

1)We show that for every code, the ratio of its list decoding radius to its minimum distance stays unchanged under the tensor product operation (rather than squaring, as one ... more >>>

We study integrality gaps for SDP relaxations of constraint satisfaction problems, in the hierarchy of SDPs defined by Lasserre. Schoenebeck recently showed the first integrality gaps for these
problems, showing that for MAX k-XOR, the ratio of the SDP optimum to the integer optimum may be as large as ... more >>>

We show that every high-entropy distribution is indistinguishable from an
efficiently samplable distribution of the same entropy. Specifically, we prove
that if $D$ is a distribution over $\{ 0,1\}^n$ of min-entropy at least $n-k$,
then for every $S$ and $\epsilon$ there is a circuit $C$ of size at most
$S\cdot ... more >>>