Costas array

A Costas array is an nxn square lattice containing n points such that each row or column contains only one point, and that all of the n(n+1)/2 vectors connecting each pair of dots are distinct.

A Costas array may be represented numerically as an nxn array of numbers, where each entry is either 1, for a point, or 0, for the absence of a point. Since each row has the constraint that it only has one point on it, Costas arrays can also be modelled as a subset of the possible permutations of n points in n positions that satisfy the extra constraints given above.

Costas arrays can be regarded as two-dimensional cousins of the one-dimensional Golomb ruler construction, and, as well as being of mathematical interest, have similar applications in phased array antennas and experimental designs.

External links

• MACTECH 1999 Programmer's challenge: Costas Arrays