Characterizing Normal Bases via the Trace Map
- In their recent article Chang et al. [Chang, Y., Troung, T. K., Reed, I. S. (2001). Normal bases over GF(q). J Algebra 241:89-101] have determined all those extensions of Galois fields for which the normal basis generators are characterized by the (obviously necessary) property of having nonzero trace. In the Present article, we present a simpler proof of a generalization of that result and discuss an application concerning the existence of trace-compatible sequences of primitive normal bases for certain primary closures of Galois fields.
| Author: | Dirk HachenbergerORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-8220 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/966 |
| Parent Title (English): | Communications in Algebra |
| Type: | Article |
| Language: | English |
| Date of Publication (online): | 2008/06/18 |
| Year of first Publication: | 2004 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2008/06/18 |
| Tag: | Cyclic Galois Extension; Finite Galois Field; Normal Basis; Normal free Element; Primitive Element; Trace; Trace-compatible Sequence |
| GND-Keyword: | Galois-Feld; Galois-Erweiterung; Spur <Mathematik>; Primitives Element |
| Volume: | 32 |
| Issue: | 1 |
| First Page: | 269 |
| Last Page: | 277 |
| DOI: | https://doi.org/10.1081/AGB-120027866 |
| 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 |
