Bent Partitions, Vectorial Dual-Bent Functions and Partial Difference Sets
Bent Partitions, Vectorial Dual-Bent Functions and Partial Difference Sets
Bent partitions of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{n}^{(p)}$ </tex-math></inline-formula> are quite powerful in constructing bent functions, vectorial bent functions and generalized bent functions, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{n}^{(p)}$ </tex-math></inline-formula> is an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> -dimensional vector space over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {F}_{p}$ </tex-math></inline-formula> , …