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/sup u+2/m) /spl times/ (2/sup u+2/n), where mn is equal to the rank of a Hadamard matrix (not restricted to be a Walsh-Hadamard Matrix) and u /spl ges/ 0. The cross-correlation function of the sequence of our construction is equal to zero, when the phase shifts k/sub x/ and k/sub y/ satisfy |k/sub x/| + |k/sub y/| < 2/sup u+1/, or max (|k/sub x/|, |k/sub y/|) /spl les/ 2/sup u/. The number of synthesized sequences is 4mn.