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 minimum weights of some dual cyclic codes.

Additional Metadata
Keywords Artin–Schreier, Character sums, Cyclic codes, Finite fields, Polynomials
Persistent URL dx.doi.org/10.1007/s10623-015-0170-7
Journal Designs, Codes and Cryptography
Citation
Wan, D. (Daqing), & Wang, Q. (2016). Index bounds for character sums of polynomials over finite fields. Designs, Codes and Cryptography, 81(3), 459–468. doi:10.1007/s10623-015-0170-7