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Gauss sums of the cubic character over \(\text{GF}(2^m)\): an elementary derivation. (English) Zbl 1215.11117
Summary: By an elementary approach, we derive the value of the Gauss sum of a cubic character over a finite field \({\mathbb F}_{2^s} \) without using Davenport-Hasse’s theorem (namely, if \(s\) is odd, the Gauss sum is \(-1\), and if \(s\) is even its value is \((-2)^\frac{s}{2}\)).

MSC:
11T24 Other character sums and Gauss sums
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