Self-dual twisted generalized Reed-Solomon codes

In this paper, by using some properties for linear algebra methods, the parity-check matrixs for twisted generalized Reed-Solomon codes with any given hook $h$ and twist $t$ are presented, and then a sufficient and necessary condition for that a twisted generalized Reed-Solomon code with dimension $h+t$ $(h\ge t)$ 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.