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

 

Primitive normal polynomials over finite fields


Authors: Ilene H. Morgan and Gary L. Mullen
Journal: Math. Comp. 63 (1994), 759-765, S19
MSC: Primary 11T06; Secondary 11T30
MathSciNet review: 1257578
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Abstract: In this note we significantly extend the range of published tables of primitive normal polynomials over finite fields. For each $ {p^n} < {10^{50}}$ with $ p \leq 97$, we provide a primitive normal polynomial of degree n over $ {F_p}$. Moreover, each polynomial has the minimal number of nonzero coefficients among all primitive normal polynomials of degree n over $ {F_p}$. The roots of such a polynomial generate a primitive normal basis of $ {F_{{p^n}}}$ over $ {F_p}$, and so are of importance in many computational problems. We also raise several conjectures concerning the distribution of such primitive normal polynomials, including a refinement of the primitive normal basis theorem.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1257578-3
PII: S 0025-5718(1994)1257578-3
Keywords: Finite field, primitive normal basis
Article copyright: © Copyright 1994 American Mathematical Society