Nonlinear network coding based on multiplication and exponentiation in GF(2m)

This article proposes a novel nonlinear network code in the GF(2m) finite field. Different from previous linear network codes that linearly mix multiple input flows, the proposed nonlinear network code mixes input flows through both multiplication and exponentiation in the GF(2m). Three relevant rules for selecting proper parameters for the proposed nonlinear network code are discussed, and the relationship between the power parameter m and the coding coefficient K is explored. Further analysis shows that the proposed nonlinear network code is equivalent to a linear network code with deterministic coefficients.