Primitive normal bases for finite fields
Authors:
H. W. Lenstra and R. J. Schoof
Journal:
Math. Comp. 48 (1987), 217231
MSC:
Primary 11T30; Secondary 12E20
MathSciNet review:
866111
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Abstract: It is proved that any finite extension of a finite field has a normal basis consisting of primitive roots.
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 [1]
 J. T. B. Beard, Jr. & K. J. West, "Some primitive polynomials of the third kind," Math. Comp., v. 28, 1974, pp. 11661167, with microfiche supplement. MR 0366879 (51:3125)
 [2]
 L. Carlitz, "Primitive roots in a finite field," Trans. Amer. Math. Soc., v. 73, 1952, pp. 373382. MR 0051869 (14:539a)
 [3]
 L. Carlitz, "Some problems involving primitive roots in a finite field," Proc. Nat. Acad. Sci. U.S.A., v. 38, 1952, pp. 314318, 618. MR 0049939 (14:250f)
 [4]
 H. Davenport, "Bases for finite fields," J. London Math. Soc., v. 43, 1968, pp. 2139; v. 44, 1969, p. 378. MR 0227144 (37:2729)
 [5]
 G. H. Hardy & E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford University Press, Oxford, 1968.
 [6]
 W. H. Mills, "The degrees of the factors of certain polynomials over finite fields," Proc. Amer. Math. Soc., v. 25, 1970, pp. 860863. MR 0263783 (41:8383)
 [7]
 O. Ore, "Contributions to the theory of finite fields," Trans. Amer. Math. Soc., v. 36, 1934, pp. 243274. MR 1501740
 [8]
 JP. Serre, Cours d'Arithmétique, Presses Universitaires de France, 1970. MR 0255476 (41:138)
 [9]
 N. Zierler, "On the theorem of Gleason and Marsh," Proc. Amer. Math. Soc., v. 9, 1958, pp. 236237. MR 0094332 (20:851)
 [10]
 N. Zierler, "On over ," Inform. and Control, v. 16, 1970, pp. 502505. MR 0271072 (42:5955)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198708661113
PII:
S 00255718(1987)08661113
Keywords:
Finite field,
normal basis,
primitive root
Article copyright:
© Copyright 1987
American Mathematical Society
