A Linear Dependence Based Construction Related to Costas Arrays

Costas arrays are special permutation patterns with various applications in communications and signal processing. Their construction is a difficult combinatorial problem and only a handful of constructions are known. Little is known about those arrays that are not generated by the existing methods. This paper presents an algorithm for the construction of sequences that obey the distinct difference constraints imposed by the Costas array problem. The algorithm is based upon the abstract linear dependence properties of various sets of simple integral vectors and their permutations. The algorithm shows that the entire Costas array problem is most naturally expressed in terms of a simple stack data structure. Simulations of the algorithm are evaluated with a linearity metric on the sequences produced.