TY - JOUR
T1 - On the construction of a primitive normal basis in a finite field
AU - Stepanov, S. A.
AU - Shparlinskii, I. E.
PY - 1990/2/28
Y1 - 1990/2/28
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).
UR - http://www.scopus.com/inward/record.url?scp=0040072829&partnerID=8YFLogxK
U2 - 10.1070/SM1990v067n02ABEH001369
DO - 10.1070/SM1990v067n02ABEH001369
M3 - Article
AN - SCOPUS:0040072829
VL - 67
SP - 527
EP - 533
JO - Mathematics of the USSR - Sbornik
JF - Mathematics of the USSR - Sbornik
SN - 0025-5734
IS - 2
ER -