Gauss Sums of the Cubic Character over GF(2m): an Elementary Derivation
Davide Schipani, Michele Elia · Bulletin of the Polish Academy of Sciences Mathematics · 2011
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 $-(-