This paper shows that, with high probability, randomly punctured Reed-Solomon codes over
fields of polynomial size achieve the list decoding capacity. More specifically, we prove that …

The recently-emerging field of higher order MDS codes has sought to unify a number of
concepts in coding theory. Such areas captured by higher order MDS codes include …

In a recent breakthrough [BGM23, GZ23, AGL23], it was shown that Reed-Solomon codes,
defined over random evaluation points, are list decodable with\emph {optimal} list size with …

Abstract Folded Reed-Solomon (FRS) codes are variants of Reed-Solomon codes, known
for their optimal list decoding radius. We show explicit FRS codes with rate R that can be list …

In this paper we take a combinatorial approach to the problem of list-decoding, which allows
us to determine the precise relation (up to the exact constant) between the decoding radius …

It is well known that no quantum error correcting code of rate R can correct adversarial errors
on more than a (1− R)/4 fraction of symbols. But what if we only require our codes to …

In this work, we consider the task of generating list-decodable codes over small (say, binary)
alphabets using as little randomness as possible. Specifically, we hope to generate codes …

We show new and improved list decoding properties of folded Reed–Solomon (RS) codes
and multiplicity codes. Both of these families of codes are based on polynomials over finite …

In this paper, we prove that explicit FRS codes and multiplicity codes achieve relaxed
generalized Singleton bounds for list size $ L\ge1. $ Specifically, we show the following:(1) …

We give a linear-time erasure list-decoding algorithm for expander codes. More precisely, let
r> 0 be any integer. Given an inner code C 0 of length d, and a d-regular bipartite expander …