The $[1,0]$-twisted generalized Reed-Solomon code

Abstract

In this paper, we not only give the parity check matrix of the $[1,0]$-twisted generalized Reed-Solomon (in short, TGRS) code, but also determine the weight distribution. Especially, we show that the $[1,0]$-TGRS code is not GRS or EGRS. Furthermore, we present a sufficient and necessary condition for any punctured code of the $[1,0]$-TGRS code to be self-orthogonal, and then construct several classes of self-dual or almost self-dual $[1,0]$-TGRS codes. Finally, basing on these self-dual or almost self-dual $[1,0]$-TGRS codes, we obtain some LCD $[1,0]$-TGRS codes.