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Golomb ruler
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==Practical applications== [[File:Golomb ruler conference room.svg|thumb|300px|Example of a conference room with proportions of a [0, 2, 7, 8, 11] Golomb ruler, making it configurable to 10 different sizes.<ref name="ErdősTurán1941"/>]] ===Information theory and error correction=== Golomb rulers are used within [[information theory]] related to [[error correcting code]]s.<ref name="titlestats.A class of binary recurrent codes with limited error propagation">{{cite journal |title=A class of binary recurrent codes with limited error propagation |date=January 1967 |journal=IEEE Transactions on Information Theory |author=Robinson J, Bernstein A |volume=13 |issue=1 |pages=106–113 |doi=10.1109/TIT.1967.1053951}}</ref> ===Radio frequency selection=== Golomb rulers are used in the selection of radio frequencies to reduce the effects of [[intermodulation interference]] with both [[Earth|terrestrial]]<ref name="titlestats.Intermodulation Interference in Radio Systems">{{cite journal |url=http://www.alcatel-lucent.com/bstj/vol32-1953/articles/bstj32-1-63.pdf |archive-url=https://web.archive.org/web/20110707104054/http://www.alcatel-lucent.com/bstj/vol32-1953/articles/bstj32-1-63.pdf |archive-date=2011-07-07 |url-status=live |title=Intermodulation Interference in Radio Systems |year=1953 |access-date=2011-03-14 |format=excerpt |doi=10.1002/j.1538-7305.1953.tb01422.x |last1=Babcock |first1=Wallace C. |journal=Bell System Technical Journal |volume=32 |pages=63–73 }}</ref> and [[outer space|extraterrestrial]]<ref name="titlestats.Carrier frequency assignment for nonlinear repeaters">{{cite journal |title=Carrier frequency assignment for nonlinear repeaters |journal=Comsat Technical Review |volume=7|pages=227 |type=abstract |bibcode=1977COMTR...7..227F |last1=Fang |first1=R. J. F. |last2=Sandrin |first2=W. A. |year=1977}}</ref> applications. ===Radio antenna placement=== Golomb rulers are used in the design of phased arrays of radio antennas. In radio astronomy one-dimensional synthesis arrays can have the antennas in a Golomb ruler configuration in order to obtain minimum redundancy of the Fourier component sampling.<ref>{{cite book |last1=Thompson |first1=A. Richard |last2=Moran |first2=James M. |last3=Swenson |first3=George W. |title=Interferometry and Synthesis in Radio Astronomy |url=https://archive.org/details/interferometrysy00thom_120 |url-access=limited |publisher=Wiley-VCH |edition=Second |year=2004 |page=[https://archive.org/details/interferometrysy00thom_120/page/n162 142] |isbn=978-0471254928}}</ref><ref>{{cite journal |last=Arsac |first=J. |title=Transmissions des frequences spatiales dans les systemes recepteurs d'ondes courtes |language=fr |trans-title=Transmissions of spatial frequencies in shortwave receiver systems |journal=Optica Acta |volume=2 |issue=112 |year=1955|pages=112–118 |doi=10.1080/713821025 |bibcode=1955AcOpt...2..112A }}</ref> ===Current transformers=== Multi-ratio [[current transformer]]s use Golomb rulers to place transformer tap points.{{citation needed|date=April 2022}}
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