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

11/08/2022

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by   Canze Zhu, et al.

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In this paper, we not only give the parity check matrix for 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.