Factorization tables for $x^{n}-1$ over $\textrm {GF} (q)$

Abstract:

These tables give the complete factorization of ${x^n} - 1$ over ${\text {GF}}(q),q = {p^a},2 \leqslant n \leqslant d$ as below, together with the Euler $\Phi$-function of ${x^n} - 1$ whenever $\Phi ({x^n} - 1) < {10^8}$. \[ \begin {array}{*{20}{c}} {q = 2;d = 32} \hfill & {q = 3;d = 27} \hfill & {q = 11;d = 15} \hfill \\ {q = {2^2};d = 16} \hfill & {q = {3^2};d = 15} \hfill & {q = 13;d = 15} \hfill \\ {q = {2^3};d = 16} \hfill & {q = 5;d = 25,n \ne {{23}^\dagger }} \hfill & {q = 17;d = 15} \hfill \\ {q = {2^4};d = 16} \hfill & {q = {5^2};d = 10} \hfill & {q = 19;d = 12} \hfill \\ {q = {2^5};d = 12} \hfill & {q = 7;d = 15} \hfill & {q = 23;d = 10} \hfill \\ \end {array} \]