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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Factorization tables for $ x\sp{n}-1$ over $ {\rm GF}\,(q)$


Authors: Jacob T. B. Beard and Karen I. West
Journal: Math. Comp. 28 (1974), 1167-1168
MSC: Primary 12C05
MathSciNet review: 0364196
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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{displaymath}\begin{array}{*{20}{c}} {q = 2;d = 32} \hfill & {q = 3;d = 27... ... {q = 7;d = 15} \hfill & {q = 23;d = 10} \hfill \\ \end{array} \end{displaymath}


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1974-0364196-5
PII: S 0025-5718(1974)0364196-5
Keywords: Factorization, Galois field, Euler $ \Phi $-function
Article copyright: © Copyright 1974 American Mathematical Society