Double Periodic Arrays with Good Correlation for Applications in Watermarking

Digital watermarking applications require constructions of double-periodic matrices with good correlations. More specifically we need as many matrix sequences as possible with both good auto and cross-correlation. Furthermore it is necessary to have double-periodic sequences with as many dots as possible. In this paper we present a method that increases the number of sequences, and another that increases the number of ones keeping the correlation good and double-periodic. Finally we combine both methods producing families of double-periodic arrays with good correlation and many dots. The method of increasing the number of sequences is due to Moreno, Omrarii and Marie. The method to increase the number of dots was started by Nguyen, Lazlo and Massey, developed by Moreno, Zhang, Kumar and Zinoviev, and further developed by Tirkel and Hall. The very nice application to digital watermarking is due to Tirkel and Hall. Finally we obtain two new constructions of optical orthogonal codes and two new constructions of matrices: Construction A which produces codes with pa-rameters (n,omega,lambda) = (p(p -1), p²-1/2, [p(p+1]), Construction B which produces families of code with parameters (n,omega,lambda) = {p²{p-1),p(p+1)/2, [p(p+1)/4]), max cross-correlation p, and family size p + 1. Contruction A´ which produces matrices with parameters (n,omega,lambda) = (p²(p-1),p(p-1),lambda_t(p) + 3) Construction B´ which produces matrices with parameters (n,omega,lambda) = (p²(p-1),p(p-1),lambda_t(p) + 3), max cross-correlation p, and family size p + 1.