The Strong Primitive Normal Basis Theorem
| dc.creator | Cohen, Stephen D. | |
| dc.creator | Huczynska, Sophie | |
| dc.date | 2006-10-12 | |
| dc.date | 2008-10-16 | |
| dc.date.accessioned | 2026-07-07T10:10:28Z | |
| dc.date.available | 2026-07-07T10:10:28Z | |
| dc.description | An element w of the extension E of degree n over the finite field F=GF(q) is called free over F if {w, w^q,...,w^{q^{n-1}}} is a (normal) basis of E/F. The Primitive Normal Basis Theorem, first established in full by Lenstra and Schoof (1987), asserts that for any such extension E/F, there exists an element w in E such that w is simultaneously primitive (i.e., generates the multiplicative group of E) and free over F. In this paper we prove the following strengthening of this theorem: aside from five specific extensions E/F, there exists an element w in E such that both w and w^{-1} are simultaneously primitive and free over F. | |
| dc.identifier | https://arxiv.org/abs/math/0610400 | |
| dc.identifier | http://arxiv.org/abs/math/0610400 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171611 | |
| dc.subject | Number Theory | |
| dc.subject | 11T30 | |
| dc.title | The Strong Primitive Normal Basis Theorem | |
| dc.type | text |