Abstract
In this paper, we give a parity check matrix of the (+)-extended twisted generalized Reed Solomon code, and then not only prove that it is MDS or NMDS, but also determine the weight distribution. Especially, based on Schur method, we show that the (+)-extended twisted generalized Reed Solomon code is neither the generalized Reed Solomon code nor extended generalized Reed Solomon code. Furthermore, we present necessary and sufficient conditions for the (+)-twisted generalized Reed Solomon code and the (+)-extended twisted generalized Reed Solomon code to be self-orthogonal, respectively. Finally, several classes of self-dual (+)-twisted generalized Reed Solomon code codes and almost self-dual (+)-extended twisted generalized Reed Solomon codes are constructed.
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