### Abstract

Let n be a natural number, q a prime power, and a primitive elementof the field GF(q^{n}). This paper shows that there exist absolute constants c_{1},c_{2}0such that for N max(exp exp(c_{1}ln^{2}n),c_{2}n lnq) the set of elements ^{1}..,^{N}includes at least one which generates a primitive normal basis of GF(q^{n}) over GF(q).For fixed n, this gives a polynomial time algorithm in lnq which, given an arbitraryprimitive element(q^{n}), finds an element which generates a primitive normalbasis for GF(q^{n}) over GF(q).

Original language | English |
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Pages (from-to) | 527-533 |

Number of pages | 7 |

Journal | Mathematics of the USSR - Sbornik |

Volume | 67 |

Issue number | 2 |

DOIs | |

Publication status | Published - 28 Feb 1990 |

Externally published | Yes |

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## Cite this

Stepanov, S. A., & Shparlinskii, I. E. (1990). On the construction of a primitive normal basis in a finite field.

*Mathematics of the USSR - Sbornik*,*67*(2), 527-533. https://doi.org/10.1070/SM1990v067n02ABEH001369