We prove the existence of Reed-Solomon codes of any desired rate $R \in (0,1)$ that are combinatorially list-decodable up to a radius approaching $1-R$, which is the information-theoretic limit. This is established by starting with the full-length $[q,k]_q$ Reed-Solomon code over a field $\mathbb{F}_q$ that is polynomially larger than the ... more >>>

One of the oldest problems in coding theory is to match the Gilbert--Varshamov bound with explicit binary codes. Over larger---yet still constant-sized---fields, algebraic-geometry codes are known to beat the GV bound. In this work, we leverage this phenomenon by taking traces of AG codes. Our hope is that the margin ... more >>>