Letbe a finite field.
a multiplicative character
be an additive character.
The Fourier transform ofin
is the Gauss sum
of module
, if both of
in
are not trivial.
The size of the instersection of a subgroup
of
with the hyperplan
is given by CSM and PF
starting point of my papers in (irreducible) cyclic codes that I have adapated in the context of abelian codes defining Gauss sums over semi-simple algebras.