Bent functions in odd characteristic can be either (weakly) regular or non-weakly regular. Furthermore one can distinguish between dual-bent functions, which are bent functions for which the dual is bent as well, and non-dual bent functions. Whereas a weakly regular bent function always has a bent dual, a non-weakly regular bent function can be either dual-bent or non-dual-bent. The classical constructions (like quadratic bent functions, Maiorana-McFarland or partial spread) yield weakly regular bent functions, but meanwhile one knows constructions of infinite classes of non-weakly regular bent functions of both types, dual-bent and non-dual-bent. In this article we focus on vectorial bent functions in odd characteristic. We first show that most p-ary bent monomials and binomials are actually vectorial constructions. In the second part we give a positive answer to the question if non-weakly regular bent functions can be components of a vectorial bent function. We present the first construction of vectorial bent functions of which the components are non-weakly regular but dual-bent, and the first construction of vectorial bent functions with non-dual-bent components.

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具有奇数特性的矢量弯曲函数及其组成

具有奇特征的弯曲函数可以是（弱）正则或非弱正则。此外，可以区分双重弯曲功能和非双重弯曲功能，双重弯曲功能是双重弯曲的弯曲功能。弱规则弯曲函数始终具有双重弯曲，非弱规则弯曲函数可以是双重弯曲或非双重弯曲。经典构造（如二次弯曲函数，Maiorana-McFarland或部分扩展）产生弱的正则弯曲函数，但是与此同时，人们知道无限类的非弱正则弯曲函数的构造，这两种类型均为双弯曲和非双弯曲。在本文中，我们重点介绍具有奇数特性的矢量弯曲函数。我们首先表明，大多数p-ary弯曲的单项式和二项式实际上是矢量构造。在第二部分中，我们对以下问题给出了肯定的答案：非弱正则弯曲函数是否可以是矢量弯曲函数的组成部分。我们介绍了矢量弯曲函数的第一个构造，其分量是非弱规则的但是双弯曲的，以及矢量弯曲函数的第一个构造是具有非双弯曲分量的。