Algebraic methods in difference sets and bent functions

Year 2021, Volume: 8 Issue: 2, 139 - 148, 20.05.2021

Pradipkumar H. Keskar Priyanka Kumari

https://doi.org/10.13069/jacodesmath.940192

https://izlik.org/JA92FJ44WD

Abstract

We provide some applications of a polynomial criterion for difference sets. These include counting the difference sets with specified parameters in terms of Hilbert functions, in particular a count of bent functions. We also consider the question about the bentness of certain Boolean functions introduced by Carlet when the $\mathcal{C}$-condition introduced by him doesn't hold.

Keywords

Hilbert functions , $\mathcal{C}$-condition , Flat , Difference set , Bent functions , Hilbert functions, $\mathcal{C}$-condition, Flat, Difference set, Bent functions

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