Families of Multidimensional Arrays with Good Autocorrelation and Asymptotically Optimal Cross-correlation

TL;DR

This paper presents a new method for constructing high-dimensional array families with optimal autocorrelation and cross-correlation properties, and demonstrates their application in digital watermarking of multimedia content.

Contribution

It introduces a novel construction of multidimensional arrays using circulant arrays of Legendre arrays, achieving asymptotically optimal cross-correlation.

Findings

Arrays exhibit asymptotically optimal pairwise cross-correlation

Application demonstrated in digital watermarking of images and videos

Construction method based on circulant arrays of Legendre arrays

Abstract

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.