On lower bounds for incomplete character sums over finite fields

The purpose of this paper is to extend results of Stepanov (1980; 1994) about lower bounds for incomplete character sums over a prime finite fieldFpto the case of arbitrary finite fieldFq.
Finite Fields and their Applications


Codes on fibre products of some Kummer coverings
Özbudak, Ferruh (Elsevier BV, 1999-04-01)
The purpose of this paper is to construct fairly long geometric Goppa codes over F-q with rather good parameters by fibre products of some Kummer coverings, This paper also extends the results of Stepanov [1] and Stepanov and Ozbudak [2]. (C) 1999 Academic Press.
Quantum system structures of quantum spaces and entanglement breaking maps
Dosi, A. A. (IOP Publishing, 2019-07-01)
This paper is devoted to the classification of quantum systems among the quantum spaces. In the normed case we obtain a complete solution to the problem when an operator space turns out to be an operator system. The min and max quantizations of a local order are described in terms of the min and max envelopes of the related state spaces. Finally, we characterize min-max-completely positive maps between Archimedean order unit spaces and investigate entanglement breaking maps in the general setting of quantum...
On maximal curves and linearized permutation polynomials over finite fields
Özbudak, Ferruh (Elsevier BV, 2001-08-08)
The purpose of this paper is to construct maximal curves over large finite fields using linearized permutation polynomials. We also study linearized permutation polynomials under finite field extensions.
On the Krall-type polynomials on q-quadratic lattices
Alvarez-Nodarse, R.; Adiguzel, R. Sevinik (Elsevier BV, 2011-08-01)
In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. In particular, the q-Racah-Krall polynomials obtained via the addition of two mass points to the weight function of the non-standard q-Racah polynomials at the ends of the interval of orthogonality are considered in detail. Some important limit cases are also discussed. (C) 2011 Royal Net...
Curves with many points and configurations of hyperplanes over finite fields
Özbudak, Ferruh (Elsevier BV, 1999-10-01)
We establish a correspondence between a class of Kummer extensions of the rational function field and configurations of hyperplanes in an affine space. Using this correspondence, we obtain explicit curves over finite fields with many rational points. Some of our examples almost attain the Oesterle bound. (C) 1999 Academic Press.
Citation Formats
F. Özbudak, “On lower bounds for incomplete character sums over finite fields,” Finite Fields and their Applications, pp. 173–191, 1996, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39441.