Costas array: Difference between revisions

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Revision as of 18:56, 20 April 2020

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==Known arrays==

All Costas array orders are known for orders 1 through 29<ref>{{harvtxt|Beard|2006}}; {{harvtxt|Drakakis|Rickard|Beard|Caballero|2008}}; {{harvtxt|Drakakis|Iorio|Rickard|2011}}; {{harvtxt|Drakakis|Iorio|Rickard|Walsh|2011}}</ref> Enumeration is as in the following table.

All Costas array orders are known for orders 1 through 29<ref name="JKB200">James K Beard, ''Generating Costas Arrays to Order 200'', 2006 40th Annual Conference on Information Sciences and Systems, (CISS) 2006, March 23, 2006, [https://doi.org/10.1109/ciss.2006.286635 DOI: 10.1109/CISS.2006.286635]</ref><ref>Konstantinos Drakakis, Scott Rickard, James K Beard, Rodrigo Caballero, Francesco Iorio, Gareth O'Brien and John Walsh, ''Results of the Enumeration of Costas Arrays of Order 27'', IEEE Transactions on Information Theory, Volume: 54, Issue: 10, Oct. 2008, [https://doi.org/10.1109/TIT.2008.928979 DOI: 10.1109/TIT.2008.928979]</ref><ref>K Drakakis, F Iorio, S Rickard, ''The enumeration of Costas arrays of order 28 and its consequences'', Adv. in Math. of Comm., 2011</ref><ref>K Drakakis, F Iorio, S Rickard, J Walsh, ''Results of the Enumeration Of Costas Arrays Of Order 29'', – Adv. in Math. of Comm., Volume 5, No. 3, 2011, 547–553, [https://dx.doi.org/10.3934/amc.2011.5.547 DOI: 10.3934/amc.2011.5.547]</ref> Enumeration is as in the following table.

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Enumeration of known Costas arrays to order 200,<ref name="JKB200"/>{{sfnp|Beard|2006}} order 500<ref>James K Beard, ''Costas array generator polynomials in finite fields'', 42nd Annual Conference on Information Sciences and Systems (CISS 2008), April 20, 2008, [https://doi.org/10.1109/CISS.2008.4558709 DOI: 10.1109/CISS.2008.455870]</ref> and to order 1030 <ref>http://jameskbeard.com/jameskbeard/Files.html#CostasArrays</ref><ref>James K Beard, "Costas arrays and enumeration to order 1030", IEEE Dataport, 2017. [Online]. Available: https://dx.doi.org/10.21227/H21P42. Accessed: Sept. 17, 2017.</ref> are available. Although these lists and databases of these Costas arrays are likely near complete, other Costas arrays with orders above 29 that are not in these lists may exist.

==Constructions==

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| url-status = dead

}}.

*{{citation

| last = Beard | first = James

| contribution = Generating Costas Arrays to Order 200

| date = March 2006

| doi = 10.1109/ciss.2006.286635

| publisher = IEEE

| title = 2006 40th Annual Conference on Information Sciences and Systems}}.

*{{citation

| last1 = Beard

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| url-status = dead

}}.

*{{citation

| last1 = Drakakis | first1 = Konstantinos

| last2 = Rickard | first2 = Scott

| last3 = Beard | first3 = James K.

| last4 = Caballero | first4 = Rodrigo

| last5 = Iorio | first5 = Francesco

| last6 = O{\textquotesingle}Brien | first6 = Gareth

| last7 = Walsh | first7 = John

| date = October 2008

| doi = 10.1109/tit.2008.928979

| issue = 10

| journal = IEEE Transactions on Information Theory

| pages = 4684–4687

| title = Results of the Enumeration of Costas Arrays of Order 27

| volume = 54}}.

*{{citation

| last1 = Drakakis | first1 = Konstantinos

| last2 = Iorio | first2 = Francesco

| last3 = Rickard | first3 = Scott

| title = The enumeration of Costas arrays of order 28 and its consequences

| journal = Advances in Mathematics of Communications

| year = 2011}}

*{{citation

| last1 = Drakakis | first1 = Konstantinos

| last2 = Iorio | first2 = Francesco

| last3 = Rickard | first3 = Scott

| last4 = Walsh | first4 = John

| date = August 2011

| doi = 10.3934/amc.2011.5.547

| issue = 3

| journal = Advances in Mathematics of Communications

| pages = 547–553

| title = Results of the enumeration of Costas arrays of order 29

| volume = 5}}.

*{{citation

| last = Gilbert | first = E. N. | authorlink = Edgar Gilbert