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Mathematics of Computation

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Normal bases via general Gauss periods

Authors: Sandra Feisel, Joachim von zur Gathen and M. Amin Shokrollahi
Journal: Math. Comp. 68 (1999), 271-290
MSC (1991): Primary 11T22; Secondary 11R18, 12E20, 12F10, 68Q40
MathSciNet review: 1484903
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Abstract: Gauss periods have been used successfully as a tool for constructing normal bases in finite fields. Starting from a primitive $r$th root of unity, one obtains under certain conditions a normal basis for $ {\mathbb F}_{q^n} $ over $ {\mathbb F}_q $, where $r$ is a prime and $nk=r-1$ for some integer $k$. We generalize this construction by allowing arbitrary integers $r$ with $nk=\varphi(r)$, and find in many cases smaller values of $k$ than is possible with the previously known approach.

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Additional Information

Sandra Feisel
Affiliation: Fachbereich 17 Mathematik-Informatik, Universität-GH Paderborn, D-33095 Paderborn, Germany

Joachim von zur Gathen

M. Amin Shokrollahi
Affiliation: International Computer Science Institute, 1947 Center Street, Berkeley, CA 94704-1198, USA

Received by editor(s): October 7, 1996
Article copyright: © Copyright 1999 American Mathematical Society