Establishing the complexity of {\em Bounded Distance Decoding} for Reed-Solomon codes is a fundamental open problem in coding theory, explicitly asked by Guruswami and Vardy (IEEE Trans. Inf. Theory, 2005). The problem is motivated by the large current gap between the regime when it is NP-hard, and the regime when ... more >>>

We study the \emph{random resolution} refutation system defined in~[Buss et al. 2014]. This attempts to capture the notion of a resolution refutation that may make mistakes but is correct most of the time. By proving the equivalence of several different definitions, we show that this concept is robust. On the ... more >>>

We initiate a systematic study of linear sketching over $\mathbb F_2$. For a given Boolean function $f \colon \{0,1\}^n \to \{0,1\}$ a randomized $\mathbb F_2$-sketch is a distribution $\mathcal M$ over $d \times n$ matrices with elements over $\mathbb F_2$ such that $\mathcal Mx$ suffices for computing $f(x)$ with high ... more >>>