Index bounds for character sums with polynomials over finite fields
Number Theory
2015-07-06 v1 Information Theory
math.IT
Abstract
We provide an index bound for character sums of polynomials over finite fields. This improves the Weil bound for high degree polynomials with small indices, as well as polynomials with large indices that are generated by cyclotomic mappings of small indices. As an application, we also give some general bounds for numbers of solutions of some Artin-Schreier equations and mininum weights of some cyclic codes.
Cite
@article{arxiv.1507.00988,
title = {Index bounds for character sums with polynomials over finite fields},
author = {Daqing Wan and Qiang Wang},
journal= {arXiv preprint arXiv:1507.00988},
year = {2015}
}