论文标题
正式的自我双重性
Formal self duality
论文作者
论文摘要
我们研究有限的阿贝尔群体中形式上的自我双重性的概念。科恩，库玛，雷赫和舒尔曼提出了有限阿贝尔团体的形式二元性。在本文中，我们给出了正式自我双重集的精确定义，并从这个角度讨论了文献中的结果。另外，我们讨论了与正式双重代码的连接。我们证明，正式的自我双重集可以简化为原始的正式自我双重集，类似于正式双重二元组的先前已知结果。此外，我们描述了正式自我双重集的几种属性。同样，本文中还提供了一些正式自我双重组的新示例。最后，我们正式研究表单$ \ {（x，f（x））\：\ x \ in \ mathbb {f} _ {2^n} \} $，其中$ f $是矢量boolean函数$ \ mathbb {f} _ {f} _ {f} _ {2^n} $ $ \ mathbb {f} _ {2^n} $。
We study the notion of formal self duality in finite abelian groups. Formal duality in finite abelian groups has been proposed by Cohn, Kumar, Reiher and Schürmann. In this paper we give a precise definition of formally self dual sets and discuss results from the literature in this perspective. Also, we discuss the connection to formally dual codes. We prove that formally self dual sets can be reduced to primitive formally self dual sets similar to a previously known result on general formally dual sets. Furthermore, we describe several properties of formally self dual sets. Also, some new examples of formally self dual sets are presented within this paper. Lastly, we study formally self dual sets of the form $\{(x,F(x)) \ : \ x\in\mathbb{F}_{2^n}\}$ where $F$ is a vectorial Boolean function mapping $\mathbb{F}_{2^n}$ to $\mathbb{F}_{2^n}$.
