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Using tools from algebraic geometry and Groebner basis theory we solve twoproblems in network coding. First we present a method to determine the smallestfield size for which linear network coding is feasible. Second we deriveimproved estimates on the success probability of random linear network coding.These estimates take into account which monomials occur in the support of thedeterminant of the product of Edmonds matrices. Therefore we finallyinvestigate which monomials can occur in the determinant of the Edmonds matrix.

On Field Size and Success Probability in Network Coding