Harmonic Analysis and a Bentness-Like Notion in Certain Finite Abelian Groups Over Some Finite Fields

Laurent Poinsot (1) , Nadia El Mrabet (2, 3, 4)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 SAS-ENSMSE - Département Systèmes et Architectures Sécurisés
3 LIASD - Laboratoire d'Informatique Avancée de Saint-Denis
4 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne

It is well-known that degree two finite field extensions can be equipped with a Hermitian-like structure similar to the extension of the complex field over the reals. In this contribution, using this structure, we develop a modular character theory and the appropriate Fourier transform for some particular kind of finite Abelian groups. Moreover we introduce the notion of bent functions for finite field valued functions rather than usual complex-valued functions, and we study several of their properties.

Mots clés: modular character theory; Hermitian-like structure; Abelian groups; Fourier transform

Domaines: Mathématiques [math]

Laurent Poinsot, Nadia El Mrabet. Harmonic Analysis and a Bentness-Like Notion in Certain Finite Abelian Groups Over Some Finite Fields. 2015. ⟨hal-01197141⟩