Reed–Solomon codes are a classic family of error-correcting codes consisting of
evaluations of low-degree polynomials over a finite field on some sequence of distinct field …

Higher order MDS codes are an interesting generalization of MDS codes recently introduced
by Brakensiek et al.,(2023). In later works, they were shown to be intimately connected to …

Folded Reed-Solomon (FRS) and univariate multiplicity codes are prominent polynomial
codes over finite fields renowned for achieving list decoding capacity. These codes have …

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 study uniquely decodable codes and list decodable codes in the high-noise regime,
specifically codes that are uniquely decodable from fraction of errors and list decodable from …

Gabidulin codes, serving as the rank-metric counterpart of Reed-Solomon codes, constitute
an important class of maximum rank distance (MRD) codes. However, unlike the fruitful …

We prove that Reed-Solomon (RS) codes with random evaluation points are list recoverable
up to capacity with optimal output list size, for any input list size. Namely, given an input list …