Modular composition is the problem of computing the coefficient vector of the polynomial $f(g(x)) \bmod h(x)$, given as input the coefficient vectors of univariate polynomials $f$, $g$, and $h$ over an underlying field $\mathbb{F}$. While this problem is known to be solvable in nearly-linear time over finite fields due to ... more >>>

We show that Reed-Solomon codes of dimension $k$ and block length $n$ over any finite field $\mathbb{F}$ can be deterministically list decoded from agreement $\sqrt{(k-1)n}$ in time $\text{poly}(n, \log |\mathbb{F}|)$.

Prior to this work, the list decoding algorithms for Reed-Solomon codes, from the celebrated results of ... more >>>

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 >>>