2005/08/02 by Andrew Z. Tirkel, Andrew Z Tirkel, Tirkel, Andrew Z +2
Computer Science · Engineering · Mathematics · #Cryptography and Security (cs.CR) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Information Theory (cs.IT) #Robotic Mechanisms and Dynamics #cs.CR #cs.DM #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.cs/0508022
arxiv created 2005/08/02 · openalex publication_date 2005/08/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper describes the synthesis of matrices with good correlation, from cyclic shifts of pseudonoise columns. Optimum matrices result whenever the shift sequence satisfies the constant difference property. Known shift sequences with the constant (or almost constant) difference property are: Quadratic (Polynomial) and Reciprocal Shift modulo prime, Exponential Shift, Legendre Shift, Zech Logarithm Shift, and the shift sequences of some m-arrays. We use these shift sequences to produce arrays for watermarking of digital images. Matrices can also be unfolded into long sequences by diagonal unfolding (with no deterioration in correlation) or row-by-row unfolding, with some degradation in correlation.