The non-GRS properties for the twisted generalized Reed-Solomon code and its extended code

Abstract: In 2017, Beelen et al. firstly introduced twisted generalized Reed-Solomon (in short, TGRS) codes, and constructed a large subclass of MDS TGRS codes. Later, they proved that TGRS code is non-GRS when the code rate is less than one half. In this letter, basing on the dual code of the TGRS code or the extended TGRS code, by using the Schur product, we prove that almost all of TGRS codes and extended TGRS codes are non-GRS when the code rate more than one half.