On Twisted Generalized Reed-Solomon Codes With ℓ Twists
Haojie Gu, Jun Zhang · IEEE Transactions on Information Theory · 2023
Abstract-In this paper, we study a class of twisted generalized Reed-Solomon (TGRS) codes with general$\ell$twists. A sufficient and necessary condition for the TGRS codes to be MDS or$\ell$-MDS$(\ell < \min \{k, n-k\})$is determined. A sufficient and necessary condition that such a TGRS code is self-dual for$\ell \leq\left\lfloor\frac{k-1}{3}\right\rfloor$is also presented. Finally, we give an explicit construction of self-dual TGRS codes.