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 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.