Factorization tables for trinomials over $\mathrm{GF}(q)$

Tables placed in the UMT file give the complete factorization over ${\text{GF}}(q),q = {p^a}$, of each trinomial $T(x)$ of degree $n, 2 \leqslant n \leqslant d$, as below, together with the generalized Euler $\Phi$-function whenever $T(x)$ is not prime and $\Phi (T(x)) < {10^8}$. In addition, the numerical exponent and q-polynomial is given for each $T(x)$ whenever $2 \leqslant n \leqslant {d_1}$.

On a microfiche card with this note, selected results from the above appear as Table I-Table IV as follows:

As evidenced by these tables, there does not necessarily exist a prime trinomial of given degree n over arbitrary ${\text{GF}}(q)$.