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A linear Fractional Network Coding (FNC) solution over Fq is a linear network coding solution over Fq in which the message dimensions need not necessarily be the same and need not be the same as the edge vector dimension. Scalar linear network coding, vector linear network coding are special cases of linear FNC. In this paper, the authors establish the connection between the existence of a linear FNC solution for a network over Fq and the represent ability over Fq of discrete polymatroids, which are the multi-set analogue of matroids. All previously known results on the connection between the scalar and vector linear solvability of networks and representations of matroids and discrete polymatroids follow as special cases.
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