Abstract :
In this correspondence, we prove that the distributions of the two-dimensional Kloosterman sums are completely determined by the distributions of the (one-dimensional) Kloosterman sums, and, by a famous result of Lauchad and Wolfman, we can give all the values of the two-dimensional Kloosterman sums. Furthermore, using the identities on one-dimensional Kloosterman sums found by Tor Helleseth and Victor Zinoviev, Hollmann and Xiang, etc., we present some new identities on Kloosterman sums in this note. Meanwhile, we also provide a new approach to producing new Kloosterman sums´ identities
Keywords :
polynomials; identities; linearized polynomial; two-dimensional Kloosterman sum distribution; Algebra; Binary codes; Binary sequences; Computer science; Frequency; Galois fields; Information analysis; Mathematics; Notice of Violation; Polynomials; Algebraic curve; Kloosterman sums; exponential sums; finite fields; linearized polynomials;
