James Beard

The Costas condition on a permutation matrix, expressed as row indices as elements of a vector c, can be expressed as A*c=b, where b is a vector of integers in which no element is zero.  A particular formulation of the matrix A allows a singular value decomposition in which the eigenvalues are squared integers and the eigenvalues may be scaled to vectors with all integer elements.  This is a database of the Costas constraint matrices A, the scaled eigenvectors, and the squared eigenvalues for orders 3 through 100.

Costas arrays are permutation matrices that meet the added Costas condition that, when used as a frequency-hop scheme, allow at most one time-and-frequency-offset signal bin to overlap another.  Databases to various orders have been available for many years.  Here we have a database that is far more extensive than any available before it.  A very powerful and easy-to-use Windows utility with a GUI accompanies the database.