arXiv:1507.00988 Abstract | arXiv Analytics

arXiv:1507.00988 [math.NT]Abstract References Reviews Resources

Index bounds for character sums with polynomials over finite fields

Published 2015-07-03Version 1

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.

Categories: math.NT, cs.IT, math.IT

Subjects: 11T24

Keywords: character sums, index bound, finite fields, small indices, high degree polynomials

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