Bent functions, partial difference sets, and quasi-Frobenius local rings
Up to now, bent functions were studied only over elementary abelian groups. The author generalizes this concept to arbitrary finite abelian groups. He then gives a characterization of finite quasi-Frobenius local rings as those finite rings which have a unique minimal (non-zero) ideal. The main part of the paper uses a maximal ideal \(M\) of such a ring \(R\) to extend bent functions and certain partial difference sets defined on \(M\times M\) to corresponding objects on \(R\times R\); in particular, he provides an inductive extension procedure for such objects over finite chain rings.
scientific article; zbMATH DE number 1515342