A simple algebraic formulation for the scalar linear network coding problem

In this work, we derive an algebraic formulation for the scalar linear network coding problem as an alternative to the one presented by Koetter et al in. Using an equivalence between network information flow and group-valued circulations, we derive a system of polynomial equations that algebraically represents the scalar linear network coding problem. Surprisingly, this system of polynomials has a maximum degree of 2. We illustrate our formulation and its advantages through example networks drawn from the literature.