Decoding Algorithms of Twisted GRS Codes and Twisted Goppa Codes
Huan Sun, Qin Yue, Xue Jia, Chengju Li · IEEE Transactions on Information Theory · 2024
In this paper, we use extended Euclid’s algorithm to propose new decoding algorithms for two classes of maximum distance separable (MDS) twisted generalized Reed-Solomon (TGRS) codes of parameters$[n, n-t, t+1]$over$\Bbb F_{q}$. For even t, the algorithms can correct$\frac {t}{2}$errors with time complexity$O(qn)$. Moreover, we also give a new decoding algorithm for a class of twisted Goppa codes. For even degree t of a Goppa polynomial, it can also correct$\frac {t}{2}$errors, which generalizes a$\lfloor \frac {t-1}{2}\rfloor $-error-correcting decoding algorithm by Sui and Yue (2023).