{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T18:26:52Z","timestamp":1787164012479,"version":"build-2736575974"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T00:00:00Z","timestamp":1665360000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T00:00:00Z","timestamp":1665360000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s10623-022-01125-0","type":"journal-article","created":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T11:03:26Z","timestamp":1665399806000},"page":"779-794","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Difference-based structural properties of costas arrays"],"prefix":"10.1007","volume":"91","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4573-5399","authenticated-orcid":false,"suffix":"Jr","given":"Bill","family":"Correll","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0629-8912","authenticated-orcid":false,"given":"Christopher N.","family":"Swanson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,10,10]]},"reference":[{"key":"1125_CR1","doi-asserted-by":"publisher","DOI":"10.21227\/H21P42","author":"JK Beard","year":"2017","unstructured":"Beard J.K.: Costas arrays and enumeration to order 1030. IEEE DataPort (2017). https:\/\/doi.org\/10.21227\/H21P42.","journal-title":"IEEE DataPort"},{"key":"1125_CR2","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1109\/TAES.2007.4285351","volume":"43","author":"JK Beard","year":"2007","unstructured":"Beard J.K., Russo J.C., Erickson K.G., Monteleone M.C., Wright M.T.: Costas array generation and search methodology. IEEE Trans. Aerosp. Electon. Syst. 43, 522\u2013538 (2007). https:\/\/doi.org\/10.1109\/TAES.2007.4285351.","journal-title":"IEEE Trans. Aerosp. Electon. Syst."},{"key":"1125_CR3","volume-title":"Introduction to Enumerative Combinatorics","author":"M B\u00f3na","year":"2005","unstructured":"B\u00f3na M.: Introduction to Enumerative Combinatorics, 1st edn McGraw-Hill, Boston (2005).","edition":"1"},{"key":"1125_CR4","doi-asserted-by":"publisher","unstructured":"Correll, Jr., B.: A closed form expression for the number of Costas arrays of arbitrary order. In: Proceedings of the forty-first asilomar conference on signals, systems, and computers, pp. 2218\u20132222, (2007) https:\/\/doi.org\/10.1109\/ACSSC.2007.4487635","DOI":"10.1109\/ACSSC.2007.4487635"},{"key":"1125_CR5","doi-asserted-by":"publisher","unstructured":"Correll, Jr., B.: A new structural property of Costas arrays. In: Proceedings of the 2018 IEEE Radar Conference, pp. 748\u2013753, (2018). https:\/\/doi.org\/10.1109\/RADAR.2018.8378653","DOI":"10.1109\/RADAR.2018.8378653"},{"key":"1125_CR6","doi-asserted-by":"publisher","unstructured":"Correll, Jr., B.: More new structural properties of Costas arrays. In: Proceedings of the 2019 IEEE radar conference, pp. 1\u20136 (2019) https:\/\/doi.org\/10.1109\/RADAR.2019.8835629","DOI":"10.1109\/RADAR.2019.8835629"},{"key":"1125_CR7","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1109\/TAES.2019.2925486","volume":"56","author":"B Correll Jr","year":"2020","unstructured":"Correll B. Jr., Beard J.K., Swanson C.N.: Costas array waveforms for closely-spaced target detection. IEEE Trans. Aerosp. Electron. Syst. 56, 1045\u20131076 (2020). https:\/\/doi.org\/10.1109\/TAES.2019.2925486.","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"1125_CR8","unstructured":"Costas, J.P.: Medium constraints on sonar design and performance. GE Co. Technical Report Class 1 Rep. R65EMH33 (1965)"},{"key":"1125_CR9","doi-asserted-by":"publisher","first-page":"996","DOI":"10.1109\/PROC.1984.12967","volume":"72","author":"JP Costas","year":"1984","unstructured":"Costas J.P.: A study of detection waveforms having nearly ideal range-Doppler ambiguity properties. Proc. IEEE 72, 996\u20131009 (1984). https:\/\/doi.org\/10.1109\/PROC.1984.12967.","journal-title":"Proc. IEEE"},{"key":"1125_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/JAM\/2006\/26385","volume":"2006","author":"K Drakakis","year":"2006","unstructured":"Drakakis K.: A review of Costas arrays. J. Appl. Math. 2006, 1\u201332 (2006).","journal-title":"J. Appl. Math."},{"key":"1125_CR11","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1109\/CISS.2006.286633","volume":"15","author":"K Drakakis","year":"2007","unstructured":"Drakakis K.: Data mining and Costas arrays. Turk. J. Elec. Engin. 15, 67\u201376 (2007). https:\/\/doi.org\/10.1109\/CISS.2006.286633.","journal-title":"Turk. J. Elec. Engin."},{"key":"1125_CR12","doi-asserted-by":"publisher","first-page":"547","DOI":"10.3934\/amc.2011.5.547","volume":"5","author":"K Drakakis","year":"2011","unstructured":"Drakakis K., Iorio F., Rickard S., Walsh J.: Results of the enumeration of Costas arrays of order 29. Adv. Math. Commun. 5, 547\u2013543 (2011). https:\/\/doi.org\/10.3934\/amc.2011.5.547.","journal-title":"Adv. Math. Commun."},{"key":"1125_CR13","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1137\/1007035","volume":"7","author":"EN Gilbert","year":"1965","unstructured":"Gilbert E.N.: Latin squares which contain no repeated diagrams. SIAM Rev. 7, 189\u2013198 (1965). https:\/\/doi.org\/10.1137\/1007035.","journal-title":"SIAM Rev."},{"key":"1125_CR14","doi-asserted-by":"publisher","first-page":"241","DOI":"10.3934\/amc.2014.8.241","volume":"8","author":"J Jedwab","year":"2014","unstructured":"Jedwab J., Wodlinger J.: Structural properties of Costas arrays. Adv. Math. Commun. 8, 241\u2013256 (2014). https:\/\/doi.org\/10.3934\/amc.2014.8.241.","journal-title":"Adv. Math. Commun."},{"key":"1125_CR15","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1016\/S0195-6698(05)80018-6","volume":"13","author":"L Lesieur","year":"1992","unstructured":"Lesieur L., Nicolas J.L.: On the Eulerian numbers $${{M}_n = \\max _{1 \\le k \\le n}{A}(n, k)}$$. Eur. J. Comb. 13, 379\u2013399 (1992). https:\/\/doi.org\/10.1016\/S0195-6698(05)80018-6.","journal-title":"Eur. J. Comb."},{"key":"1125_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.37236\/5610","volume":"23","author":"CN Swanson","year":"2016","unstructured":"Swanson C.N., Correll B. Jr., Ho R.W.: Enumeration of Parallelograms in Permutation Matrices for Improved Bounds on the Density of Costas arrays. Electron. J. Comb. 23, 1\u201314 (2016). https:\/\/doi.org\/10.37236\/5610.","journal-title":"Electron. J. Comb."},{"key":"1125_CR17","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2022.3202507","author":"L Warnke","year":"2022","unstructured":"Warnke L., Correll B. Jr., Swanson C.N.: The density of Costas Arrays decays exponentially. IEEE Trans. Inf. Theory (2022). https:\/\/doi.org\/10.1109\/TIT.2022.3202507.","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01125-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-022-01125-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01125-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T13:18:42Z","timestamp":1678454322000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-022-01125-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,10]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["1125"],"URL":"https:\/\/doi.org\/10.1007\/s10623-022-01125-0","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,10]]},"assertion":[{"value":"15 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 September 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no conflicts of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"Not applicable.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}]}}