On Hadamard matrices and bent functions

Using the generalized Kronecker construction of binary Hadamard matrices, we build Hadamard matrices of square order, which keep many properties of the original matrices. When one of the initial matrices is normalized and linear, the resulting Hadamard matrix is regular and gives a bent function in each row, or in each column, or both. When both initial Hadamard matrices are normalized and linear, we can construct bent functions with maximal algebraic degree. In this case, we compute the dimension of the kernel and an upper bound for the rank.