Gauss Sums of the Cubic Character over ${\rm GF}(2^m)$: an Elementary Derivation
Volume 59 / 2011
Bulletin Polish Acad. Sci. Math. 59 (2011), 11-18
MSC: Primary 12Y05; Secondary 12E30.
DOI: 10.4064/ba59-1-2
Abstract
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 $-(-2)^{s/2}$).
