Twisted generalized Reed-Solomon (TGRS) codes are generalizations of generalized Reed-Solomon (GRS) codes. It is widely recognized that GRS codes are maximum distance sparable (MDS) codes, but TGRS codes are not necessarily MDS. In this paper, we give a condition that is both sufficient and necessary for twisted generalized Reed-Solomon codes with general twists (-TGRS codes) to be MDS. For -TGRS codes to be self-dual, we also propose a condition that is both sufficient and necessary. Furthermore, we consider three special cases of twists and present two new and explicit constructions of self-dual -TGRS codes.
No takes yet. Share an insight, caveat, or question.
Ding et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: