6 papers
On Proximity Gaps for One-Point Algebraic Geometric Codes
Songsong Li, Chaoping Xing, Chen Yuan +1
Proximity gaps and correlated agreement underpin the soundness of interactive oracle proofs. We establish these properties for general one-point algebraic geometry (AG) codes, exte…
List Size of Random Linear Codes: Optimality and the Limits of Average-Radius List Decoding
Chen Yuan, Ruiqi Zhu
Guruswami, Li, Mosheiff, Resch, Silas and Wootters conjectured that, for every fixed prime power and , random linear codes of rate have li…
A Syndrome--Space Approach to Proximity Gaps and Correlated Agreement for Random Linear Codes and Random Reed--Solomon Codes
Chen Yuan, Ruiqi Zhu
Proximity gaps and correlated agreement have become central tools in the analysis of interactive oracle proofs of proximity (IOPPs) and code-based SNARKs. Informally, a proximity-g…
Explicit List-Decodable Linearized Reed-Solomon and Folded Linearized Reed-Solomon Subcodes
Kuo Shang, Chen Yuan, Ruiqi Zhu
The sum-rank metric is the mixture of the Hamming and rank metrics. The sum-rank metric found its application in network coding, locally repairable codes, space-time coding, and qu…
Improvement of the Gilbert-Varshamov Bound for Linear Codes and Quantum Codes
Chen Yuan, Ruiqi Zhu
The Gilbert--Varshamov (GV) bound is a central benchmark in coding theory, establishing existential guarantees for error-correcting codes and serving as a baseline for both Hamming…
List Decoding of Reed-Solomon Codes and Folded Reed-Solomon Codes Over Galois Ring
Chen Yuan, Ruiqi Zhu
List decoding of codes can be seen as the generalization of unique decoding of codes while list decoding over finite fields has been extensively studied, extending these results to…