Costas array

In mathematics, a Costas array can be regarded <a href="/facts/Geometry/wTQf5ffQ">geometrically</a> as a set of n points, each at the center of a <a href="/facts/Square/JHJeMvmL">square</a> in an n×n <a href="/facts/Square_tiling/3ym86mvv">square tiling</a> such that each row or column contains only one point, and all of the n(n − 1)/2 <a href="/facts/Displacement_(vector)/jkmEfS3C">displacement</a> <a href="/facts/Euclidean_vector/bCLrdksy">vectors</a> between each pair of dots are distinct. This results in an ideal "thumbtack" auto-<a href="/facts/Ambiguity_function/5uTy0kn4">ambiguity function</a>, making the arrays useful in applications such as <a href="/facts/Sonar/0Rg2G40e">sonar</a> and <a href="/facts/Radar/jk9BTbFA">radar</a>. Costas arrays can be regarded as two-dimensional cousins of the one-dimensional <a href="/facts/Golomb_ruler/DlVkTL1H">Golomb ruler</a> construction, and, as well as being of mathematical interest, have similar applications in <a href="/facts/Experimental_design/VMrNftbr">experimental design</a> and <a href="/facts/Phased_array/5wvA9WLV">phased array</a> radar engineering.
Costas arrays are named after <a href="/facts/John_P._Costas_(engineer)/F8H7IosW">John P. Costas</a>, who first wrote about them in a 1965 technical report. Independently, <a href="/facts/Edgar_Gilbert/r6g0Tlun">Edgar Gilbert</a> also wrote about them in the same year, publishing what is now known as the logarithmic Welch method of constructing Costas arrays.
The general enumeration of Costas arrays is an open problem in computer science and finding an algorithm that can solve it in polynomial time is an open research question.

Costas array open-in-new

Costas array