Abstract
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. However, the best possible parameters for these problems are still unknown, and in this paper, we take a step in this direction. We show the existence of RS codes that are list-decodable or list-recoverable beyond the Johnson radius for every rate, with a polynomial field size in the block length. In particular, we show that for every ϵ(0,1) there exist RS codes that are list-decodable from radius 1-ϵ and rate less than ϵ/2-ϵ, with constant list size. We deduce our results by extending and strengthening a recent result of Ferber, Kwan, and Sauermann on puncturing codes with large minimum distance and by utilizing the underlying code's linearity.
| Original language | English |
|---|---|
| Pages (from-to) | 2261-2268 |
| Number of pages | 8 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 69 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1 Apr 2023 |
Keywords
- Johnson radius
- List-decoding
- list-recovery
- reed-solomon codes
All Science Journal Classification (ASJC) codes
- Information Systems
- Library and Information Sciences
- Computer Science Applications