Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for a special type of bent functions, so-called Niho bent functions there is a more general equivalence relation called o-equivalence which is induced from the equivalence of o-polynomials. In the present work we study, for a given o-polynomial, a general construction which provides all possible o-equivalent Niho bent functions, and we considerably simplify it to a form which excludes EA-equivalent cases. That is, we identify all cases which can potentially lead to pairwise EA-inequivalent Niho bent functions derived from o-equivalence of any given Niho bent function. Furthermore, we determine all pairwise EA-inequivalent Niho bent functions arising from all known o-polynomials via o-equivalence.

布尔函数，特别是弯曲函数，被认为是所谓的EA等价性，它是最常用的保持函数弯曲性的等价关系。但是，对于特殊类型的折弯函数，即所谓的Niho折弯函数，存在一个更一般的等价关系，称为o-等价关系，它是由o多项式的等价关系引起的。在当前工作中，我们研究一个给定的o多项式，它提供了所有可能的o等效的Niho弯曲函数的一般构造，并且我们将其简化为排除EA等效情况的形式。也就是说，我们确定了所有可能导致源自任何给定Niho弯曲函数的o等效性的成对EA不等价Niho弯曲函数的所有情况。此外，