Self-dual twisted generalized Reed-Solomon codes

In this paper, by using some properties for linear algebra methods, the parity-check matrices for twisted generalized Reed-Solomon codes with any given hook $h$ and twist $t$ are presented, and then a sufficient and necessary condition for the twisted generalized Reed-Solomon code with $h\ge t$ to be self-dual is given. Furthermore, several classes of self-dual codes with small Singleton defect are constructed based on twisted generalized Reed-Solomon codes, especially some of these self-dual codes are MDS or NMDS.