The characterization of hyper-bent function with multiple trace terms in the extension field
<|reference_start|>The characterization of hyper-bent function with multiple trace terms in the extension field: Bent functions are maximally nonlinear Boolean functions with an even number of variables, which include a subclass of functions, the so-called hyper-bent functions whose properties are stronger than bent functions and a complete classification of hyper-bent functions is elusive and inavailable.~In this paper,~we solve an open problem of Mesnager that describes hyper-bentness of hyper-bent functions with multiple trace terms via Dillon-like exponents with coefficients in the extension field~$\mathbb{F}_{2^{2m}}$~of this field~$\mathbb{F}_{2^{m}}$. By applying M\"{o}bius transformation and the theorems of hyperelliptic curves, hyper-bentness of these functions are successfully characterized in this field~$\mathbb{F}_{2^{2m}}$ with~$m$~odd integer.<|reference_end|>
@article{han2024the,
    title={The characterization of hyper-bent function with multiple trace terms in
  the extension field},
    author={Peng Han, Keli Pu},
    journal={arXiv preprint arXiv:2407.01946},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.01946},
    primaryClass={cs.IT math.IT}
}