Lower Bounds on Two-Dimensional Generalized Orthogonal Sequences

For various applications in image, communications and signal processing, two-dimensional (2-D) generalized orthogonal (GO) sequences, that is, 2-D sequences with zero correlation zone (ZCZ) and 2-D complementary orthogonal (CO) sequences with ZCZ, are widely investigated. New lower bounds for 2-D GO sequences, based on matrix theory on rank, are derived and presented, some examples that attain these lower bounds are given. As a direct application to our results, upper bound on family size of 2-D mutually complementary orthogonal (MCO) codes defined by Luke [9] is proposed.