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 …

In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS codes as a
generalization of MDS codes. An order-ℓ MDS code, denoted by MDS (ℓ), has the property …

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 …

Understanding the limits of list-decoding and list-recovery of Reed-Solomon (RS) codes is of
prime interest in coding theory and has attracted a lot of attention in recent decades …

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 …

Random linear codes (RLCs) are well known to have nice combinatorial properties and near-
optimal parameters in many different settings. However, getting explicit constructions …

The splitting-off operation in undirected graphs is a fundamental reduction operation that
detaches all edges incident to a given vertex and adds new edges between the neighbors of …

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 consider hypergraph network design problems where the goal is to construct a
hypergraph that satisfies certain connectivity requirements. For graph network design …

In this paper, we prove that with high probability, random Reed-Solomon codes approach
the half-Singleton bound-the optimal rate versus error tradeoff for linear insdel codes-with …