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

I. D. Svalbe, A. Z. Tirkel

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5 Citations (Scopus)


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 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.

Original languageEnglish
Article number18
Number of pages19
JournalEURASIP Journal on Advances in Signal Processing
Issue number1
Publication statusPublished - 1 Dec 2017


  • Correlation
  • Digital watermarks
  • Discrete projection
  • Finite Radon transform
  • Pseudo-noise arrays

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