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A condition governing the possibility and impossibility of linear independence among the global encoding kernels of a linear network code is found. Based on this condition, we propose several alternative definitions of generic network codes, which give interpretations of such codes from different perspectives. We also present a unified framework for specifying and constructing different classes of linear network codes. Finally, using the insight obtained from the unified framework, we show that the proofs of some existing results regarding generic network codes can be greatly simplified.