On ternary Kloosterman sums modulo 12.

Finite Fields and Their Applications 14 (2008), 1083-1090.

Let K(a) denote the Kloosterman sum on F_{3m}.
It is easy to see that K(a)=2 (mod 3) for all a in F_{3m}.
We completely characterize those a in F_{3m}
for which
K(a)=1 (mod 2), K(a)=0 (mod 4)
and K(a)=2 (mod 4). The simplicity of the characterization
allows us to count the number of
the a in F_{3m}
belonging to each of these three classes.
As a byproduct we offer an alternative
proof for a new class of quasi-perfect
ternary linear codes recently presented by Danev and Dodunekov.