Hermitian Self-Dual MDS Twisted Generalized Reed–Solomon Codes

Self-dual MDS codes over finite fields constitute an important family of linear codes with broad applications in combinatorics and cryptography. Twisted generalized Reed–Solomon (TGRS) codes are capable of simultaneously possessing the MDS property and self-duality. In this paper, we derive necessary and sufficient conditions for general TGRS codes to be Hermitian self-dual. Using a new Hermitian-type partition, we develop three families of Hermitian self-dual TGRS codes whose evaluation points are taken from additive cosets, corresponding to code lengths $n|q-1,n=q$ and $n=2\sqrt{q}$. We further give another novel Hermitian self-dual construction relying on multiplicative cosets for length $n=q+1$. Additionally, we establish necessary and sufficient conditions for TGRS codes to be Hermitian self-dual MDS codes and present an explicit construction for this class of codes.