Two dimensional binary sequences exhibiting diamond shaped zero correlation zone

A two-dimensional binary sequence is used as a two-dimensional bar-codes, a position detection patterns, a diffraction pattern for calibration of a LASER beam, and so on. We have reported a two-dimensional binary sequence with wide range of zero-correlation [1]. We developed synthesis methods for several different classes of two-dimensional binary sequence with diamond shaped zero-correlation zone. In this paper, we show the construction of these sequence and the their properties. The area of the zero-correlation zone of the sequence is almost twice as the area of the zero-correlation, zone of previous reported sequences. The size of synthesized sequence is (2(u+2)m) x (2(u+2)n), where mn is equal to the rank of a Hadamard matrix (not restricted to be a Walsh-Hadamard Matrix) and u greater than or equal to 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)\) less than or equal to 2(u). The number of synthesized sequences is 4mn.