An exposition of recent list-size bounds of FRS Codes
Abhibhav Garg, Prahladh Harsha, Mrinal Kumar, Ramprasad, Saptharishi, Ashutosh Shankar
TL;DR
This paper provides a concise overview of recent significant advancements in the combinatorial list-size bounds of Folded Reed Solomon (FRS) codes, highlighting key results from recent research efforts.
Contribution
It offers a clear exposition of the latest improvements in list-size bounds of FRS codes achieved by multiple recent studies.
Findings
Significant improvements in list-size bounds of FRS codes.
Simplifications of previous proofs and bounds.
Unified presentation of recent key results.
Abstract
In the last year, there have been some remarkable improvements in the combinatorial list-size bounds of Folded Reed Solomon codes and multiplicity codes. Starting from the work on Kopparty, Ron-Zewi, Saraf and Wootters (SIAM J. Comput. 2023) (and subsequent simplifications due to Tamo (IEEE Trans. Inform. Theory 2024), we have had dramatic improvements in the list-size bounds of FRS codes due to Srivastava (SODA 2025) and Chen & Zhang (STOC 2025). In this note, we give a short exposition of these three results (Tamo, Srivastava and Chen-Zhang).
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Advanced Wireless Communication Techniques