Matrix Construction Using Cyclic Shifts of a Column

Abstract

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.