Normal bases in finite fields via general Gauss periods

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 $ 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


Publié dans:
Mathematics of Computation, 68, 225, 271-290
Année
1999
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 Notice créée le 2007-01-26, modifiée le 2018-03-17

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