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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01197141
Contributor : Nadia El Mrabet <>
Submitted on : Friday, September 11, 2015 - 11:20:13 AM
Last modification on : Thursday, March 14, 2019 - 7:58:57 PM
Long-term archiving on : Tuesday, December 29, 2015 - 12:25:47 AM

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

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