Research Paper#Coding Theory, Error Correction, Decoding Algorithms🔬 ResearchAnalyzed: Jan 3, 2026 16:45
Efficient Decoding Algorithms for Non-GRS Codes
Published:Dec 30, 2025 13:27
•1 min read
•ArXiv
Analysis
This paper addresses the important problem of decoding non-Generalized Reed-Solomon (GRS) codes, specifically Twisted GRS (TGRS) and Roth-Lempel codes. These codes are of interest because they offer alternatives to GRS codes, which have limitations in certain applications like cryptography. The paper's contribution lies in developing efficient decoding algorithms (list and unique decoding) for these codes, achieving near-linear running time, which is a significant improvement over previous quadratic-time algorithms. The paper also extends prior work by handling more complex TGRS codes and provides the first efficient decoder for Roth-Lempel codes. Furthermore, the incorporation of Algebraic Manipulation Detection (AMD) codes enhances the practical utility of the list decoding framework.
Key Takeaways
- •Develops efficient decoding algorithms for Twisted GRS (TGRS) and Roth-Lempel codes.
- •Achieves near-linear running time for decoding, improving upon previous quadratic-time complexity.
- •Extends prior work by handling more complex TGRS codes (up to O(n^2) twists).
- •Provides the first efficient decoder for Roth-Lempel codes.
- •Incorporates Algebraic Manipulation Detection (AMD) codes into the list-decoding framework.
Reference
“The paper proposes list and unique decoding algorithms for TGRS codes and Roth-Lempel codes based on the Guruswami-Sudan algorithm, achieving near-linear running time.”