On twisted generalized Reed-Solomon codes with l twists

In this paper, we study a class of twisted generalized Reed-Solomon (TGRS) codes with general l twists. A sufficient and necessary condition for the TGRS codes to be MDS or l-MDS (l<k and l<n-k) is determined. A sufficient and necessary condition that such a TGRS code is self-dual for 3l<k-1 is also presented. Finally, we give an explicit construction of self-dual TGRS codes. And examples of self-dual MDS TGRS codes for small l are given.