Two dimensional binary sequences exhibiting diamond shaped zero correlation zone

A two-dimensional binary sequence is used as a two-dimensional bar-code, a position detection pattern, a diffraction pattern for calibration of a laser beam, etc.. We have reported a two-dimensional binary sequence with wide range of zero-correlation. We developed synthesis methods for several different classes of two-dimensional binary sequence with diamond shaped zero-correlation zone. We show the construction of these sequences and the their properties. The area of the zero-correlation zone of the sequence is almost twice the area of the zero-correlation zone of previously reported sequences. The size of the synthesized sequence is (2^u+2m) × (2^u+2n), where mn is equal to the rank of a Hadamard matrix (not restricted to be a Walsh-Hadamard Matrix) and u ≥ 0. The cross-correlation function of the sequence of our construction is equal to zero, when the phase shifts k_x and k_y satisfy |k_x| + |k_y| < 2^u+1, or max (|k_x|, |k_y|) ≤ 2^u. The number of synthesized sequences is 4mn.