Abstract: We present a 3D array construction with application to video watermarking. This new construction uses two main ingredients: an extended rational cycle (ERC) as a shift sequence and a Legendre array as a base. This produces a family of 3D arrays with good auto and cross-correlation. We calculate exactly the values of the auto correlation and the cross-correlation function and their frequency. We present a unified method of obtaining multivariate recursion polynomials and their footprints for all finite multidimensional arrays. Also, we describe new results for arbitrary arrays and enunciate a result for arrays constructed using the method of composition. We also show that the size of the footprint is invariant under dimensional transformations based on the Chinese Remainder Theorem.

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