Geometric and design-theoretic aspects of semibent functions. I (Q1960226)

This paper considers semibent functions \(f\) and uses them to geometrically construct certain \((2^{2n}, 2^{2n-1} - 2^{n-1}, 2^{2n-1} - 2^n)\) BIBDs. Some properties of the automorphism groups of these designs are also examined. When \(f\) has a linear structure, these designs are two copies of a symmetric \((2^{2n}, 2^{2n-1} - 2^{n-1}, 2^{2n-2} - 2^{n-1})\) BIBD.