Self-dual twisted generalized Reed-Solomon codes

Abstract

In this paper, by using some properties for linear algebra methods, the paritycheck 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 ≥ 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.

Two new classes of Hermitian self-orthogonal non-GRS MDS codes and their applications

“…Starting from TGRS codes, several classes of LCD non-GRS MDS codes were presented in [33]. Euclidean self-dual TGRS codes have also been constructed, e.g., in [21,43]. Very recently, Zhu and Liao [44] proposed the constructions of Euclidean self-orthogonal TGRS codes.…”