We study challenge codes for physically unclonable functions (PUFs). Starting from the classical Hadamard challenge code, we augment it by one vector. Numerical values suggest that the optimal choice of this vector for maximizing the entropy is to pick a vector the farthest away from the code formed by the challenges and their binary complements. This leads us to study the covering radius of Hadamard codes. A notion of bent sequence that generalizes the classical notion from Hadamard matrices of Sylvester type to general Hadamard matrices is given. Lower bounds for Paley-type Hadamard matrices are given.