New self-dual codes from TGRS codes with general $ \ell $ twists

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 $ \ell $ twists ($ \ell $-TGRS codes) to be MDS. For $ \ell $-TGRS codes to be self-dual, we also propose a condition that is both sufficient and necessary. Furthermore, we consider three special cases of $ \ell $ twists and present two new and explicit constructions of self-dual $ \ell $-TGRS codes.