On the construction of a primitive normal basis in a finite field

S. A. Stepanov; I. E. Shparlinskii

doi:10.1070/SM1990v067n02ABEH001369

On the construction of a primitive normal basis in a finite field

S. A. Stepanov, I. E. Shparlinskii

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Let n be a natural number, q a prime power, and a primitive elementof the field GF(qⁿ). This paper shows that there exist absolute constants c₁,c₂0such that for N max(exp exp(c₁ln²n),c₂n lnq) the set of elements ¹..,^Nincludes at least one which generates a primitive normal basis of GF(qⁿ) over GF(q).For fixed n, this gives a polynomial time algorithm in lnq which, given an arbitraryprimitive element(qⁿ), finds an element which generates a primitive normalbasis for GF(qⁿ) over GF(q).

Original language	English
Pages (from-to)	527-533
Number of pages	7
Journal	Mathematics of the USSR - Sbornik
Volume	67
Issue number	2
DOIs	https://doi.org/10.1070/SM1990v067n02ABEH001369
Publication status	Published - 28 Feb 1990
Externally published	Yes

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N2 - Let n be a natural number, q a prime power, and a primitive elementof the field GF(qn). This paper shows that there exist absolute constants c1,c20such that for N max(exp exp(c1ln2n),c2n lnq) the set of elements 1..,Nincludes at least one which generates a primitive normal basis of GF(qn) over GF(q).For fixed n, this gives a polynomial time algorithm in lnq which, given an arbitraryprimitive element(qn), finds an element which generates a primitive normalbasis for GF(qn) over GF(q).

AB - Let n be a natural number, q a prime power, and a primitive elementof the field GF(qn). This paper shows that there exist absolute constants c1,c20such that for N max(exp exp(c1ln2n),c2n lnq) the set of elements 1..,Nincludes at least one which generates a primitive normal basis of GF(qn) over GF(q).For fixed n, this gives a polynomial time algorithm in lnq which, given an arbitraryprimitive element(qn), finds an element which generates a primitive normalbasis for GF(qn) over GF(q).

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