The Status of Costas Arrays

The definition, the basic properties, and all the currently known systematic constructions for Costas arrays are presented, as well as a table of the number C(n) of Costas arrays of order n, for 2 les n les 26. It is proved that lim sup_nrarrinfin C(n) = infin, and the conjecture liminf_nrarrinfin C(n) = 0 is discussed. A Costas array of order n is known to be equivalent to a permutation {1,2,...,n} for which the difference triangle contains no repeated elements in any row. A generalized Costas array of order n = q-1(or n=q -2) is defined as a permutation of the nonzero elements (or also excluding 1) of the q-element field for which the difference triangle contains no repeated elements in any row. Two new constructions for these generalized Costas arrays are described and illustrated.