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

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