Two dimensional binary sequences exhibiting diamond shaped zero correlation zone

Abstract

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+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.