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.

翻译：本文使用线性代数方法的某些属性,介绍了带有任何特扣美元和曲折美元的扭曲通用Reed-Solomon代码的等值检查矩阵,然后提供了使带有美元和特元的扭曲通用Reed-Solomon代码具有自我性的充足和必要条件,此外,根据扭曲通用Reed-Solomon代码,特别是其中一些自译自审代码是MDS或NDDS。