Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and
cloud storage systems about nine years ago. A lot of progress on the study of LRCs has …

Locally decodable codes are error-correcting codes that admit efficient decoding algorithms;
any bit of the original message can be recovered by looking at only a small number of …

This book explains some recent applications of the theory of polynomials and algebraic
geometry to combinatorics and other areas of mathematics. One of the first results in this …

Locally correctable codes (LCCs) and locally testable codes (LTCs) are error-correcting
codes that admit local algorithms for correction and detection of errors. Those algorithms are …

We study the list-decodability of multiplicity codes. These codes, which are based on
evaluations of high-degree polynomials and their derivatives, have rate approaching 1 while …

For every integer $ r\geq 2$ and every $\epsilon> 0$, we construct an explicit infinite family
of quantum LDPC codes supporting a transversal $ C^{r-1} Z $ gate with length $ N …

This book introduces important results and techniques in property testing, where the goal is
to design algorithms that decide whether their input satisfies a predetermined property in …

We describe a new parameterized family of symmetric error-correcting codes with low-
density parity-check matrices (LDPC). Our codes can be described in two seemingly …

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 …

Abstract Recently, Kumar and Mon reached a significant milestone by constructing
asymptotically good relaxed locally correctable codes (RLCCs) with poly-logarithmic query …