Algebraic methods in difference sets and bent functions

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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