On the differential and Walsh spectra of $x^2q+1$ over $\mathbbF_q^2$
<|reference_start|>On the differential and Walsh spectra of $x^2q+1$ over $\mathbbF_q^2$: Let $q$ be an odd prime power and let $\mathbb{F}_{q^2}$ be the finite field with $q^2$ elements. In this paper, we determine the differential spectrum of the power function $F(x)=x^{2q+1}$ over $\mathbb{F}_{q^2}$. When the characteristic of $\mathbb{F}_{q^2}$ is $3$, we also determine the value distribution of the Walsh spectrum of $F$, showing that it is $4$-valued, and use the obtained result to determine the weight distribution of a $4$-weight cyclic code.<|reference_end|>
@article{mesnager2024on,
    title={On the differential and Walsh spectra of $x^{2q+1}$ over
  $\mathbb{F}_{q^2}$},
    author={Sihem Mesnager and Huawei Wu},
    journal={arXiv preprint arXiv:2407.07710},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.07710},
    primaryClass={cs.CR cs.IT math.IT math.NT}
}