= Linearized polynomial over a finite field
{title2=$L(X)=\sum_{i=0}^d a_iX^{q^i}$}
= q-linearized polynomial
{synonym}
Over a <field> containing $\mathbb F_q$, a sum of $q$-power monomials is $\mathbb F_q$-linear. If its leading coefficient and linear coefficient are nonzero, its root space has exactly $q^d$ elements and dimension $d$ over $\mathbb F_q$. Automorphisms of its <splitting field> act faithfully and linearly on that root space, embedding the <Galois group> in $GL(d,q)$.
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