In 2017, Zhang et al. proposed a question (not open problem) and two open problems in [IEEE TIT 63 (8): 5336--5349, 2017] about constructing bent functions by using Rothaus' construction. In this note, we prove that the sufficient conditions of Rothaus' construction are also necessary, which answers their question. Besides, we demonstrate that the second open problem, which considers the iterative method of constructing bent functions by using Rothaus' construction, has only a trivial solution. It indicates that all bent functions obtained by using Rothaus' construction iteratively can be generated from the direct sum of an initial bent function and a quadratic bent function. This directly means that Zhang et al.'s construction idea makes no contribution to the construction of bent functions. To compensate the weakness of their work, we propose an iterative construction of bent functions by using a secondary construction in [DCC 88: 2007--2035, 2020].

翻译：2017年，张等人于[IEEE TIT 63 (8): 5336--5349, 2017]中提出了一个疑问（非公开问题）及两个关于利用Rothaus构造构建bent函数的公开问题。本文证明了Rothaus构造的充分条件同时也是必要条件，从而解答了其疑问。此外，我们论证了第二个公开问题——即关于利用Rothaus构造迭代构建bent函数的方法——仅存在平凡解。这表明所有通过迭代应用Rothaus构造获得的bent函数，均可由初始bent函数与二次bent函数的直和生成。这直接意味着张等人的构造思路对bent函数的构建并无贡献。为弥补其工作的不足，我们基于[DCC 88: 2007--2035, 2020]中的次级构造，提出了一种bent函数的迭代构造方法。