Normal Bases and Completely Free Elements in Prime Power Extensions over Finite Fields

Author: Hachenberger D.

Source: Finite Fields and Their Applications, Volume 2, Number 1, January 1996 , pp. 21-34(13)

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Abstract:

We continue the work of the previous paper (Hachenberger, Finite Fields Appl. , in press), and, generalizing some of the results obtained there, we give explicit constructions of free and completely free elements in GF( q r n ) over GF( q ), where n is any nonnegative integer and where r is any odd prime number which does not divide the characteristic of GF( q ) or where r = 2 and q = 1 mod 4. Together with results on the case where r = 2 and q = 3 mod 4 obtained in the previous paper and results on the well-known case where r is equal to the characteristic of GF( q ), we are able to explicitly determine free and completely free elements in GF( q m ) over GF( q ) for every nonnegative integer m and every prime power q .

Language: English

Document Type: Research article

Affiliations: Institut fur Mathematik der Universitat Augsburg, Universitatsstrasse 14, Augsburg, D-86135, Germany

Publication date: 1996-01-01