Arrays composed from the extended rational cycle | Zendy

Domingo GómezPérez | Zendy; Ana I. Gómez | Zendy; Andrew Z. Tirkel | Zendy

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Arrays composed from the extended rational cycle

Author(s) -

Domingo GómezPérez,

Ana I. Gómez,

Andrew Z. Tirkel

Publication year - 2017

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2017024

Subject(s) - mathematics , recursion (computer science) , chinese remainder theorem , legendre polynomials , invariant (physics) , sequence (biology) , rational function , remainder , cross correlation , algorithm , pure mathematics , arithmetic , mathematical analysis , biology , mathematical physics , genetics

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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