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 <italic>every</italic> 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) | 1 |
| Number of pages | 1 |
| Journal | IEEE Transactions on Information Theory |
| DOIs | |
| State | Accepted/In press - 2022 |
Keywords
- Codes
- Decoding
- Hamming distances
- Johnson radius
- Linearity
- list-decoding
- list-recovery
- Reed-Solomon codes
- Reed-Solomon codes
- Research and development
- Upper bound