On Parity-Check Matrices of Twisted Generalized Reed–Solomon Codes

Twisted Generalized Reed-Solomon (TGRS) Codes are a class of linear codes which contain MDS codes but are not equivalent to GRS code. In recent years, many scholars have studied the construction of MDS self-dual codes through TGRS code. Among these works, the number of twists is actually quite small, and an important step in showing a TGRS code is self-dual is to find its parity-check matrix. In this paper, we focus on the computation of parity-check matrices of TGRS codes with almost no restrictions on twist and hook vectors. By application of elementary row (column) operations in linear algebra, we present a unified but elementary approach to obtain the parity-check matrices of TGRS codes. This paper creates a foundation for further study of MDS self-dual TGRS codes on a much broader scope.