Set of marks on a 2d square grid such that no two pairs of marks are the same distance apart
In mathematics, a Costas array can be regarded geometrically as a set of n points, each at the center of a square in an n×n square tiling such that each row or column contains only one point, and all of the n(n − 1)/2 displacement vectors 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, 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.[1]
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 (1965); Gilbert (1965); An independent discovery of Costas arrays, Aaron Sterling, October 9, 2011.
applications in experimental design and phased array radar engineering. Costasarrays are named after John P. Costas, who first wrote about them in a 1965 technical...
standard array in coding theory An array or matrix (mathematics) a Costasarray a Monge array A holor In statistics, arrays are a name for some kinds of...
application of Costas loops is in wireless receivers. Its advantage over other PLL-based detectors is that at small deviations the Costas loop error voltage...
values. Golomb rulers can be viewed as a one-dimensional special case of Costasarrays. The Golomb ruler was named for Solomon W. Golomb and discovered independently...
Mathematical game Mathematical puzzle No-three-in-line problem Rook polynomial Costasarray The number of combinations of 8 squares from 64 is the binomial coefficient...
all of whose columns and rows each have exactly one nonzero element. A Costasarray is a special case of a permutation matrix. An incidence matrix in combinatorics...
\kappa _{P}} , which is also the sign of ρ P {\displaystyle \rho _{P}} . Costasarray, a permutation matrix in which the displacement vectors between the entries...
(engineer) (1923–2008), American engineer, invented the Costas loop and Costasarrays John P. Costas (business) (born 1957), American businessman, former...
as the Tunkhannock Viaduct John P. Costas – electrical engineer, inventor of the Costas loop and the Costasarray Wayne Hale – NASA engineer Mamoon Hamid...
created in this way (and their circular shifts) have been shown to be Costasarrays. If n is a positive integer, the integers from 1 to n − 1 that are coprime...
nucleic acid sequences in the target. The original nucleic acid arrays were macro arrays approximately 9 cm × 12 cm and the first computerized image based...
classical Steiner tree problem. Gilbert discovered Costasarrays independently of and in the same year as Costas,[G65] and is also known for his work with John...
and the entries are the competing players or teams. Bent functions Costasarrays Factorial designs A frequency square (F-square) is a higher order generalization...
magrodome-covered pool areas and other features that would allow travel to a wide array of destinations. The ship also had the same platform as sister line Carnival's...
of array elements. For a planar array, the computation of directivity is more complicated and requires consideration of the positions of each array element...
variations in the gain of individual elements of the image sensor array. Maria Petrou, Costas Petrou (2010) Image Processing: The Fundamentals. John Wiley...
WagerWeb.com is a Costa Rica–based sports book that offers betting lines on an array of sporting and media related events. Founded in 1994, the company...
2017. Retrieved February 2, 2017. Brady, Erik (February 9, 2017). "Bob Costas steps down as NBC host of Olympics; Mike Tirico to replace him". USA Today...
Retrieved 2021-09-27. Irakli, Maria N.; Samanidou, Victoria F.; Biliaderis, Costas G.; Papadoyannis, Ioannis N. (July 2012). "Simultaneous determination of...
Gardner, Bryant Gumbel, Greg Gumbel, Jim Lampley, Bob Costas NBC Sunday Night Football – Bob Costas, Dan Patrick, Keith Olbermann, Liam McHugh, Mike Tirico...
Best Paper Award, 2018 "Costas Spanos". CITRIS and the Banatao Institute. Archived from the original on 2020-10-21. "Prof. Costas Spanos Is the Interim...
measuring 4.1 m (13 ft) by 2.7 m (8 ft 10 in) with a total array of 120 m2 (1,300 sq ft). The Solar arrays are 2 in number. It could offer around 3-4 times more...
challenged the conquistadores. Many thousands more quickly succumbed to the vast array of Old World pathogens and infectious diseases that their systems had no...
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