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We introduce a construction for families of 2n-dimensional arrays with asymptotically optimal pairwise cross-correlation. These arrays are constructed using a circulant array of n-dimensional Legendre arrays. We also introduce an application of these higher-dimensional arrays to high-capacity digital watermarking of images and video.arXiv:2001.08894v2 fatcat:r52ov4vpovbc7kws5jr4zphkga