Index bounds for character sums with polynomials over finite fields

2015/07/03 by Daqing Wan, Qiang Wang, Wan, Daqing +1
Computer Science · Engineering · Mathematics · #11T24 #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1507.00988

openalex publication_date 2015/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• An improvement to the Hasse–Weil bound and applications to character sums, cryptography and coding

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• The additive index of polynomials over finite fields
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