Multi-dimensional arrays for watermarking

This paper presents two new classes of families of multi-periodic arrays suitable for digital watermarking. These families are large and all arrays have good auto and cross-correlation, and are available in many sizes. The construction is based on log quadratic and exponential quadratic maps. The maps applied to elements in an extension field on a natural multi-dimensional grid. The grid also leads to a generalized multi-dimensional Legendre array, which can be used in the family constructions.