Combinatorial designs with Costas arrays properties

Abstract

Several constructions for 0–1 three-dimensional arrays, in which some of the two-dimensional subarrays have ‘good’ two-dimensional autocorrelation function values, i.e., the vectors connecting two 1's in the matrix are all distinct as vectors, are given. Some of those constructions lead to constructions of Vatican squares in which each symbol defines a Costas array.