A generalization of Gauss sums and its applications to Siegel modular forms and L-functions associated with the vector space of quadratic forms.
A large family of Boolean functions
In a series of papers many Boolean functions with good cryptographic properties were constructed using number-theoretic methods. We construct a large family of Boolean functions by using polynomials over finite fields, and study their cryptographic properties: maximum Fourier coefficient, nonlinearity, average sensitivity, sparsity, collision and avalanche effect.
A matrix paraphrase of cyclotomy
A new cubic character sum
A note on evaluations of some exponential sums
1. Introduction. The recent article [1] gives explicit evaluations for exponential sums of the form where χ is a non-trivial additive character of the finite field , odd, and . In my dissertation [5], in particular in [4], I considered more generally the sums S(a,N) for all factors N of . The aim of the present note is to evaluate S(a,N) in a short way, following [4]. We note that our result is also valid for even q, and the technique used in our proof can also be used to evaluate certain...
A note on Waring's problem in finite fields
A note on weight enumerators of linear self-dual codes.
A Stickelberger theorem for p-adic Gauss sums
Approximation of the discrete logarithm in finite fields of even characteristic by real polynomials
We obtain lower bounds on degree and additive complexity of real polynomials approximating the discrete logarithm in finite fields of even characteristic. These bounds complement earlier results for finite fields of odd characteristic.
Arrangements d'hyperplans et sommes de Gauss
Arrangements with one Bounded component and p-adic integrals.
Character sums in finite fields
Complete arcs arising from a generalization of the Hermitian curve
We investigate complete arcs of degree greater than two, in projective planes over finite fields, arising from the set of rational points of a generalization of the Hermitian curve. The degree of the arcs is closely related to the number of rational points of a class of Artin-Schreier curves, which is calculated by using exponential sums via Coulter's approach. We also single out some examples of maximal curves.
Coverings of Singular curves over Finite Fields.
Cyclotomic numbers of order 2l, l an odd prime
Détermination géométrique des sommes de Selberg-Evans
Estimates for Soto-Andrade sums.
Explicit evaluations of some Weil sums
Exponential sums for O¯(2n,q) and their applications
Exponential sums for symplectic groups and their applications