We give a unified hidden-derivative framework for list decoding and mutual correlated agreement of ordinary Reed--Solomon codes over prime fields, on arbitrary prescribed evaluation sets. For every fixed slack $\gamma>0$, every sufficiently large block length $n$, every prime $q\ge n$, and every dimension $1\le k\le(1-\gamma)n$, a deterministic algorithm finds all ... more >>>

We present a general framework for derandomizing random linear codes with respect to a broad class of permutation-invariant properties, known as local properties, which encompass several standard notions such as distance, list-decoding, list-recovery, and perfect hashing. Our approach extends the classical Alon-Edmonds-Luby (AEL) construction through a modified formalism of local ... more >>>

Understanding the power and limitations of classical and quantum information, and how they differ, is an important endeavor. On the classical side, property testing of distributions is a fundamental task: a tester, given samples of a distribution over a typically large domain such as $\{0,1\}^n$, is asked to verify properties ... more >>>