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 \({\mathbb {F}}_{2^{n}}\).

我们研究有限阿贝尔群中形式自二元性的概念。Cohn、Kumar、Reiher 和 Schürmann 已经提出了有限阿贝尔群中的形式对偶性。在本文中，我们给出了形式自对偶集的精确定义，并从这个角度讨论了文献中的结果。此外，我们还讨论了与正式对偶代码的联系。我们证明形式自对偶集可以简化为原始形式自对偶集，类似于先前已知的一般形式对偶集的结果。此外，我们描述了形式自对偶集的几个属性。此外，本文还介绍了形式自对偶集的一些新示例。最后，我们正式学习形式为\(\{(x,F(x)) \ : \ x\in {\mathbb {F}}_{2^{n}}\}\) 的自对偶集，其中F是一个向量布尔函数映射\({\mathbb {F}}_{2^{n}}\)到\({\mathbb {F}}_{2^{n}}\)。