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In mathematics, a '''Costas array''' can be regarded [[geometry|geometrically]] as a set of ''n'' points lying on the [[Square (geometry)|square]]s of a ''n''×''n'' [[checkerboard]], such that each row or column contains only one point, and that all of the ''n''(''n'' − 1)/2 [[displacement (vector)|displacement]] [[vector (geometric)|vector]]s between each pair of dots are distinct. This results in an ideal 'thumbtack' auto-[[ambiguity function]], making the arrays useful in applications such as [[sonar]] and [[radar]]. 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 [[experimental design]] and [[phased array]] radar engineering.
Costas arrays are named after [[John P. Costas (engineer)|John P. Costas]], who first wrote about them in a 1965 technical report. Independently, [[Edgar Gilbert]] also wrote about them in the same year, publishing what is now known as the logarithmic Welch method of constructing Costas arrays.<ref>{{citation
| last = Gilbert | first = E. N. | authorlink = Edgar Gilbert | doi = 10.1137/1007035 | issue = 2 | journal = SIAM Review | jstor = 2027267 | pages = 189–198 | title = Latin squares which contain no repeated digrams | volume = 7 | year = 1965}}.<ref>[http://nanoexplanations.wordpress.com/2011/10/09/an-independent-discovery-of-costas-arrays/ An independent discovery of Costas arrays], Aaron Sterling, October 9, 2011.</ref> ==Numerical representation==
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Enumeration of known Costas arrays to order 200<ref name="JKB200"/>, order 500<ref>
==Constructions==
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