Extended families of 2D arrays with near optimal auto and low cross-correlation

I. D. Svalbe, A. Z. Tirkel
2017 EURASIP Journal on Advances in Signal Processing  
Families of 2D arrays can be constructed where each array has perfect autocorrelation, and the cross-correlation between any pair of family members is optimally low. We exploit equivalent Hadamard matrices to construct many families of p p × p arrays, where p is any 4k-1 prime. From these families, we assemble extended families of arrays with members that exhibit perfect autocorrelation and next-to-optimally low cross-correlation. Pseudo-Hadamard matrices are used to construct extended families
more » ... using p = 4k + 1 primes. An optimal family of 31 31 × 31 perfect arrays can provide copyright protection to uniquely stamp a robust, low-visibility watermark within every frame of each second of high-definition, 30 fps video. The extended families permit the embedding of many more perfect watermarks that have next-to-minimal cross-correlations.
doi:10.1186/s13634-017-0455-2 fatcat:6qdgfwc2k5hopbirav2wkemm7i