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There Are Infinitely Many Bent Functions for Which the Dual Is Not Bent

机译：有无限个弯曲函数，对偶不弯曲

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摘要

Bent functions can be classified into regular bent functions, weakly regular but not regular bent functions, and non-weakly regular bent functions. Regular and weakly regular bent functions always appear in pairs, since their duals are also bent functions. In general, this does not apply to non-weakly regular bent functions. However, the first known construction of non-weakly regular bent functions by Çeşmelioğlu et al. yields bent functions for which the dual is also bent. In this paper, the first construction of non-weakly regular bent functions for which the dual is not bent is presented. We call such functions non-dual-bent functions. Until now, only sporadic examples found via computer search were known. We then show that with the direct sum of bent functions and with the construction by Çeşmelioğlu et al., one can obtain infinitely many non-dual-bent functions once one example of a non-dual-bent function is known.
机译：弯曲函数可分为常规弯曲函数，弱常规但不常规弯曲函数和非弱常规弯曲函数。规则和弱规则弯曲函数始终成对出现，因为它们的对偶也是弯曲函数。通常，这不适用于非弱常规弯曲功能。然而，Çeşmelioğlu等人的第一个已知的非弱正则弯曲函数的构造。产生对偶也被弯曲的弯曲函数。在本文中，提出了对偶不弯曲的非弱正则弯曲函数的第一种构造。我们称这种功能为非双弯曲功能。到现在为止，只有通过计算机搜索找到的零星示例是已知的。然后我们证明，利用弯曲函数的直接总和以及Çeşmelioğlu等人的构造，一旦已知一个非双弯曲函数的实例，就可以无限地获得许多非双弯曲函数。

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