On ternary Kloosterman sums modulo 12

摘要

Let K(a) denote the Kloosterman sum on F_(3~m). It is easy to see that K (a) ≡ 2 (mod 3) for all a ∈ F_(3~m). We completely characterize those a ∈ F_(3~m) 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 ∈ F_(3~m) 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.