In coding theory, list recoverability is a fundamental concept which robustly captures how ``spread-out'' codewords are in a code.
More formally, given a code $C \subseteq \Sigma^n$ and input lists $S_1, \hdots, S_n \subseteq \Sigma$ of size at most $\ell$, list recoverability requires that there are at most $L$ codewords ... more >>>

We extend the recent work of Reis and Rothvoss on sparsifying sums of $\ell_1$ norms to the more general task of sparsifying (Minkowski) sums of centrally symmetric, convex sets. As our main result, we prove that for any $\varepsilon > 0$ and centrally symmetric, convex sets $C_1, \ldots, C_m\subseteq\mathbb R^n$ ... more >>>

We give new explicit constructions of several fundamental objects in linear-algebraic pseudorandomness and combinatorics, including lossless rank extractors, weak subspace designs, and strong $s$-blocking sets over finite fields.

Our focus is on the small-field regime, where the field size depends only on a secondary parameter (such as the rank or ... more >>>