We study the 2-ary constraint satisfaction problems (2-CSPs), which can be stated as follows: given a constraint graph $G = (V, E)$, an alphabet set $\Sigma$ and, for each edge $\{u, v\} \in E$, a constraint $C_{uv} \subseteq \Sigma \times \Sigma$, the goal is to find an assignment $\sigma: V ... more >>>

We show that popular hardness conjectures about problems from the field of fine-grained complexity theory imply structural results for resource-based complexity classes. Namely, we show that if either k-Orthogonal Vectors or k-CLIQUE requires $n^{\epsilon k}$ time, for some constant $\epsilon > 1/2$, to count (note that these conjectures are significantly ... more >>>

In this work, we show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent advances in coding theory. Folded Reed-Solomon codes were the first explicit constructions ... more >>>