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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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