Improved Decoding Algorithms for MDS and Almost-MDS Codes From Twisted GRS Codes

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 decodin...

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Vydáno v:IEEE transactions on information theory Ročník 71; číslo 10; s. 7688 - 7698
Hlavní autoři: Wang, Guodong, Liu, Hongwei, Luo, Jinquan
Médium: Journal Article
Jazyk:angličtina
Vydáno: IEEE 01.10.2025
Témata:
almost-MDS code
Codes
Decoding
decoding algorithm
Finite element analysis
Generators
Linear codes
MDS code
Polynomials
Reed-Solomon codes
Sun
Training
Twisted generalized Reed-Solomon code
twisted Goppa code
Vectors
ISSN:0018-9448, 1557-9654
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Popis
Shrnutí: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. Moreover, these two optimized decoding algorithms can be applied to the decoding of a more general class of twisted Goppa codes.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2025.3594174