Normal bases and completely free elements in prime power extensions over finite fields
- 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.
| Author: | Dirk HachenbergerORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-8497 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/993 |
| Parent Title (English): | Finite Fields and Their Applications |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 1996 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2008/06/19 |
| Tag: | normal bases; free elements; completely free elements; finite fields; prime power extensions |
| GND-Keyword: | Galois-Feld; Galois-Erweiterung; Basis <Mathematik> |
| Volume: | 2 |
| Issue: | 1 |
| First Page: | 21 |
| Last Page: | 34 |
| DOI: | https://doi.org/10.1006/ffta.1996.0002 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Diskrete Mathematik, Optimierung und Operations Research | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
