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Over a finite field $\mathbb{F}_{q^m}$, the evaluation of skew polynomials isintimately related to the evaluation of linearized polynomials. This connectionallows one to relate the concept of polynomial independence defined for skewpolynomials to the familiar concept of linear independence for vector spaces.This relation allows for the definition of a representable matroid called the$\mathbb{F}_{q^m}[x;\sigma]$-matroid, with rank function that makes it a metricspace. Specific submatroids of this matroid are individually bijectivelyisometric to the projective geometry of $\mathbb{F}_{q^m}$ equipped with thesubspace metric. This isometry allows one to use the$\mathbb{F}_{q^m}[x;\sigma]$-matroid in a matroidal network coding application.

Matroidal Structure of Skew Polynomial Rings with Application to Network Coding