Factorization tables for $x^{n}-1$ over $\textrm {GF} (q)$
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- by Jacob T. B. Beard and Karen I. West PDF
- Math. Comp. 28 (1974), 1167-1168 Request permission
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 $\Phi ({x^n} - 1) < {10^8}$. \[ \begin {array}{*{20}{c}} {q = 2;d = 32} \hfill & {q = 3;d = 27} \hfill & {q = 11;d = 15} \hfill \\ {q = {2^2};d = 16} \hfill & {q = {3^2};d = 15} \hfill & {q = 13;d = 15} \hfill \\ {q = {2^3};d = 16} \hfill & {q = 5;d = 25,n \ne {{23}^\dagger }} \hfill & {q = 17;d = 15} \hfill \\ {q = {2^4};d = 16} \hfill & {q = {5^2};d = 10} \hfill & {q = 19;d = 12} \hfill \\ {q = {2^5};d = 12} \hfill & {q = 7;d = 15} \hfill & {q = 23;d = 10} \hfill \\ \end {array} \]References
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J. T. B. BEARD, JR., "Computing in ${\text {GF}}(q)$," Math. Comp., this issue.
- Jacob T. B. Beard Jr. and Karen I. West, Some primitive polynomials of the third kind, Math. Comp. 28 (1974). MR 366879, DOI 10.1090/S0025-5718-1974-0366879-X
- Oystein Ore, Contributions to the theory of finite fields, Trans. Amer. Math. Soc. 36 (1934), no.Β 2, 243β274. MR 1501740, DOI 10.1090/S0002-9947-1934-1501740-7
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 1167-1168
- MSC: Primary 12C05
- DOI: https://doi.org/10.1090/S0025-5718-1974-0364196-5
- MathSciNet review: 0364196