An improvement on Weil bounds for character sums of polynomials over finite fields

Let \(\mathbb {F}_q\) ${\mathbb{F}}_q$ be a finite field with q elements, where q is a power of a prime p. In this paper, we obtain an improvement on Weil bounds for character sums associated to a polynomial f(x) over \(\mathbb {F}_q \) ${\mathbb{F}}_q$ , which extends the results of Wan et al. (Des. Codes Cryptogr. 81, 459–468, 2016) and Wu et al. (Des. Codes Cryptogr. 90, 2813–2821, 2022).