Improved Decoding Algorithms for MDS and Almost-MDS Codesfrom Twisted GRS Codes
Guodong Wang, Hongwei Liu, Jinquan Luo
TL;DR
This paper develops improved decoding algorithms for twisted GRS codes and almost-MDS TGRS codes, enhancing efficiency over previous methods by providing precise key equation characterizations and tailored decoding procedures.
Contribution
It introduces new decoding algorithms for TGRS and almost-MDS TGRS codes with better performance and detailed key equation characterizations.
Findings
Decoding algorithms outperform previous methods in efficiency.
Precise key equation characterizations for TGRS codes.
Enhanced decoding for almost-MDS TGRS codes.
Abstract
In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further study decoding of almost-MDS TGRS codes and provide a decoding algorithm. These two decoding algorithms are more efficient in terms of performance compared with the decoding algorithms presented in [Sun et al., IEEE-TIT, 2024] and [Sui et al., IEEE-TIT, 2023] respectively.
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Taxonomy
TopicsCoding theory and cryptography · Advanced Wireless Communication Techniques · Cryptography and Residue Arithmetic