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Recently, Network Error Correction coding (NEC) has been studied extensively. Several bounds in classical coding theory have been extended to network error correction coding, especially the Singleton bound. In this paper, following the research line using the extended global encoding kernels proposed in, the refined Singleton bound of NEC can be proved more explicitly. Moreover, the authors give a constructive proof of the attainability of this bound and indicate that the required field size for the existence of network Maximum Distance Separable (MDS) codes can become smaller further.
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