We obtain geometric characterizations of the dual functions for quadratic bent and vectorial bent functions in terms of quadrics. Additionally, using the zeros of the polynomial \(X^{q+1}+X+a\) which have been studied recently in the literature, we provide some examples of binomial quadratic bent functions on \(\mathbb {F}_{q^4}\) and \(\mathbb {F}_{q^6}\), where q is a power of 2.

中文翻译：

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二次弯曲函数及其对偶

我们根据二次曲线获得了二次弯曲和矢量弯曲函数的对偶函数的几何特征。此外，使用最近在文献中研究的多项式\(X^{q+1}+X+a\)的零点，我们提供了一些关于\(\mathbb {F}_ {q^4}\)和\(\mathbb {F}_{q^6}\)，其中q是 2 的幂。