This paper is about the proximity gaps phenomenon for Reed-Solomon codes.
Very roughly, the proximity gaps phenomenon for a code $\mathcal C \subseteq \mathbb F_q^n$ says that for two vectors $f,g \in \mathbb F_q^n$, if sufficiently many linear combinations $f + z \cdot g$ (with $z \in \mathbb F_q$) ... more >>>

A large alphabet Locally Decodable Code (LDC) $C:\Sigma^{k} \to \Sigma'^{n}$, where $\Sigma'$ may be large, is a code where each symbol of $x$ can be decoded by making few queries to a noisy version of $C(x)$. The rate of $C$ is its information rate, namely $\frac{k \log (|\Sigma|) }{n \log ... more >>>

In a breakthrough in the long-going attempt to construct good explicit tree codes, Cohen, Haeupler and Schulman (CHS) (STOC 2018) constructed constant-distance tree codes with rate 1/O(log log n). In their construction a large-alphabet tree code is used as a core element - and they were able to utilize polynomials ... more >>>