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

S. A. Stepanov, I. E. Shparlinskii

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)527-533
Number of pages7
JournalMathematics of the USSR - Sbornik
Volume67
Issue number2
DOIs
Publication statusPublished - 28 Feb 1990
Externally publishedYes

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