Packing Costas Arrays

Abstract

A Costas latin square of order n is a set of n disjoint Costas arrays of the same order. Costas latin squares are studied here from a construction as well as a classification point of view. A complete classification is carried out up to order 27. In this range, we verify the conjecture that there is no Costas latin square for any odd order n ≥ 3. Various other related combinatorial structures are also considered, including near Costas latin squares (which are certain packings of near Costas arrays) and Vatican Costas squares.