{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T18:23:54Z","timestamp":1761675834778,"version":"3.41.0"},"reference-count":32,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2011,2,1]],"date-time":"2011-02-01T00:00:00Z","timestamp":1296518400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001602","name":"Science Foundation Ireland","doi-asserted-by":"publisher","award":["05\/Y12\/I67706\/MI\/00608\/RFP\/MTH1164"],"award-info":[{"award-number":["05\/Y12\/I67706\/MI\/00608\/RFP\/MTH1164"]}],"id":[{"id":"10.13039\/501100001602","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2011,2]]},"abstract":"<jats:p>\n            A Costas array is an arrangement of\n            <jats:italic>N<\/jats:italic>\n            dots on an\n            <jats:italic>N<\/jats:italic>\n            -by-\n            <jats:italic>N<\/jats:italic>\n            grid, one per row, one per column, such that no two dots share the same displacement vector with any other pair. Costas arrays have applications in SONAR\/RADAR systems, communication systems, cryptography, and other areas. We present a standardization of notation and language which can be used to discuss Costas array generation techniques and array manipulations. Using this standardization we can concisely and clearly state various theorems about Costas arrays, including several new theorems about the symmetries of Costas arrays. We also define labels for each array (generated, emergent, and sporadic), which describe whether the array is generated using a known technique, generated using a semiempirical variation of a known technique, or of unexplained origin. A new method for obtaining emergent Costas arrays, the DRT expansion, is also given here for the first time. A MATLAB Costas array toolbox has also been developed which implements the proposed standardization. The toolbox contains a comprehensive set of functions covering Costas array generation, manipulation and classification.\n          <\/jats:p>","DOI":"10.1145\/1916461.1916465","type":"journal-article","created":{"date-parts":[[2011,3,3]],"date-time":"2011-03-03T08:44:26Z","timestamp":1299141866000},"page":"1-31","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["Costas Arrays"],"prefix":"10.1145","volume":"37","author":[{"given":"Ken","family":"Taylor","sequence":"first","affiliation":[{"name":"University College Dublin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Scott","family":"Rickard","sequence":"additional","affiliation":[{"name":"University College Dublin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Konstantinos","family":"Drakakis","sequence":"additional","affiliation":[{"name":"University College Dublin"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2011,2]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_1_1_1","DOI":"10.1109\/JPROC.2008.2011947"},{"doi-asserted-by":"publisher","key":"e_1_2_1_2_1","DOI":"10.1109\/CISS.2006.286635"},{"doi-asserted-by":"publisher","key":"e_1_2_1_3_1","DOI":"10.1109\/CISS.2008.4558709"},{"volume-title":"Proceedings of the IEEE Radar Conference. 260--265","author":"Beard J.","key":"e_1_2_1_4_1"},{"volume-title":"Proceedings of the IEEE International Symposium on Information Theory. 405","author":"Brown C.","key":"e_1_2_1_5_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_6_1","DOI":"10.1109\/PROC.1987.13761"},{"key":"e_1_2_1_7_1","first-page":"143","article-title":"Primitive elements in finite fields and Costas arrays","volume":"2","author":"Cohen S.","year":"1991","journal-title":"Appl. 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Large sets of frequency hopped waveforms with nearly ideal orthogonality properties. M.S. thesis. MIT Cambridge MA. Rickard S. 1993. Large sets of frequency hopped waveforms with nearly ideal orthogonality properties. M.S. thesis. MIT Cambridge MA.","key":"e_1_2_1_26_1","DOI":"10.1121\/1.407613"},{"volume-title":"Proceedings of the IMA International Conference on Mathematics in Signal Processing.","year":"2004","author":"Rickard S.","key":"e_1_2_1_27_1"},{"volume-title":"Proceedings of the 40th Annual Conference on Information Sciences and Systems.","author":"Rickard S.","key":"e_1_2_1_28_1"},{"volume-title":"Proceedings of the IMA International Conference on Mathematics in Signal Processing.","author":"Taylor K.","key":"e_1_2_1_29_1"},{"unstructured":"Taylor K. Rickard S. and Drakakis K. 2008b. Costas arrays MATLAB toolbox. www.costasarrays.org. Taylor K. Rickard S. and Drakakis K. 2008b. Costas arrays MATLAB toolbox. www.costasarrays.org.","key":"e_1_2_1_30_1"},{"volume":"1","volume-title":"Proceedings of the Military Communications Conference (MILCOM): Communications for Network-Centric Operations: Creating the Information Force.","author":"Westbrook L.","key":"e_1_2_1_31_1"},{"volume-title":"Proceedings of the 40th Annual Conference on Information Sciences and Systems.","author":"Xin","key":"e_1_2_1_32_1"}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1916461.1916465","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1916461.1916465","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T21:14:53Z","timestamp":1750281293000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1916461.1916465"}},"subtitle":["Survey, Standardization, and MATLAB Toolbox"],"short-title":[],"issued":{"date-parts":[[2011,2]]},"references-count":32,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,2]]}},"alternative-id":["10.1145\/1916461.1916465"],"URL":"https:\/\/doi.org\/10.1145\/1916461.1916465","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"type":"print","value":"0098-3500"},{"type":"electronic","value":"1557-7295"}],"subject":[],"published":{"date-parts":[[2011,2]]},"assertion":[{"value":"2009-07-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-09-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-02-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}