Formal self duality

Abstract We study the notion of formal self duality in finite abelian groups. Formal groups has been proposed by Cohn, Kumar, Reiher and Schürmann. In this paper we give a precise definition formally dual sets discuss results from literature perspective. Also, connection to codes. prove that can be reduced primitive similar previously known result on general sets. Furthermore, describe several properties some new examples are presented within paper. Lastly, form $\{(x,F(x)) \ : x\in {\mathbb {F}}_{2^{n}}\}$ { ( x , F ) : ∈ 2 n } where F is vectorial Boolean function mapping ${\mathbb {F}}_{2^{n}}$ .