A permutation array is a square binary matrix that contains a single 1 by row and by column. Costas arrays are permutation arrays where the vectors connecting two entries with 1 are distinct. These arrays are useful in applications such as radar and sonar, digital watermarking, and wireless communications in general. In this talk, we will present a generalization of Costas arrays to multiple dimensions, extend the Welch and Lempel constructions to multiple dimensions, and study some of their properties.
