{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:21:33Z","timestamp":1740122493274,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2023,5,6]],"date-time":"2023-05-06T00:00:00Z","timestamp":1683331200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,6]],"date-time":"2023-05-06T00:00:00Z","timestamp":1683331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62172319","U19B2021"],"award-info":[{"award-number":["62172319","U19B2021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program","doi-asserted-by":"crossref","award":["2021YFA000503"],"award-info":[{"award-number":["2021YFA000503"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2023,8]]},"DOI":"10.1007\/s10623-023-01230-8","type":"journal-article","created":{"date-parts":[[2023,5,6]],"date-time":"2023-05-06T07:01:45Z","timestamp":1683356505000},"page":"2769-2778","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The q-ary Golay arrays of size $$2\\times 2\\times \\cdots \\times 2$$ are standard"],"prefix":"10.1007","volume":"91","author":[{"given":"Erzhong","family":"Xue","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1525-3356","authenticated-orcid":false,"given":"Zilong","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,5,6]]},"reference":[{"key":"1230_CR1","doi-asserted-by":"publisher","first-page":"1048","DOI":"10.1109\/18.42220","volume":"35","author":"S Alquaddoomi","year":"1989","unstructured":"Alquaddoomi S., Scholtz R.A.: On the nonexistence of Barker arrays and related matters. IEEE Trans. Inf. Theory 35, 1048\u20131057 (1989).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"246","key":"1230_CR2","doi-asserted-by":"publisher","first-page":"967","DOI":"10.1090\/S0025-5718-03-01576-X","volume":"73","author":"PB Borwein","year":"2004","unstructured":"Borwein P.B., Ferguson R.A.: A complete description of Golay pairs for lengths up to $$100$$. Math. Comput. 73(246), 967\u2013985 (2004).","journal-title":"Math. Comput."},{"key":"1230_CR3","first-page":"273","volume-title":"Communication Theory","author":"RH Barker","year":"1953","unstructured":"Barker R.H.: Group synchronizing of binary digital systems. In: Jackson W. (ed.) Communication Theory, pp. 273\u2013287. Academic Press, New York (1953)."},{"key":"1230_CR4","doi-asserted-by":"publisher","first-page":"2663","DOI":"10.1007\/s10623-021-00938-9","volume":"89","author":"J Chai","year":"2021","unstructured":"Chai J., Wang Z., Xue E.: Walsh spectrum and Nega spectrum of complementary arrays. Des. Codes Cryptogr. 89, 2663\u20132677 (2021).","journal-title":"Des. Codes Cryptogr."},{"key":"1230_CR5","doi-asserted-by":"publisher","first-page":"2011","DOI":"10.1090\/S0002-9939-07-08703-5","volume":"135","author":"JA Davis","year":"2007","unstructured":"Davis J.A., Jedwab J., Smith K.W.: Proof of the Barker array conjecture. Proc. Am. Math. Soc. 135, 2011\u20132018 (2007).","journal-title":"Proc. Am. Math. Soc."},{"issue":"7","key":"1230_CR6","doi-asserted-by":"publisher","first-page":"2397","DOI":"10.1109\/18.796380","volume":"45","author":"JA Davis","year":"1999","unstructured":"Davis J.A., Jedwab J.: Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes. IEEE Trans. Inf. Theory 45(7), 2397\u20132417 (1999).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1230_CR7","volume-title":"Abstract Algebra","author":"DS Dummit","year":"2004","unstructured":"Dummit D.S., Foote R.M.: Abstract Algebra, 3rd edn Wiley, New York (2004).","edition":"3"},{"key":"1230_CR8","unstructured":"Dymond, M., Barker: Arrays: Existence, Generalization and Alternatives. PhD thesis, University of London, London (1992)"},{"issue":"9","key":"1230_CR9","doi-asserted-by":"publisher","first-page":"4261","DOI":"10.1109\/TIT.2006.880024","volume":"52","author":"F Fiedler","year":"2006","unstructured":"Fiedler F., Jedwab J.: How do more Golay sequences arise? IEEE Trans. Inf. Theory 52(9), 4261\u20134266 (2006).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"1230_CR10","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1016\/j.jcta.2007.10.001","volume":"115","author":"F Fiedler","year":"2008","unstructured":"Fiedler F., Jedwab J., Parker M.G.: A multi-dimensional approach to the construction and enumeration of Golay complementary sequences. J. Combin. Theory Ser. A 115(5), 753\u2013776 (2008).","journal-title":"J. Combin. Theory Ser. A"},{"issue":"7","key":"1230_CR11","doi-asserted-by":"publisher","first-page":"3114","DOI":"10.1109\/TIT.2008.924667","volume":"54","author":"F Fiedler","year":"2008","unstructured":"Fiedler F., Jedwab J., Parker M.G.: A framework for the construction of Golay sequences. IEEE Trans. Inf. Theory 54(7), 3114\u20133129 (2008).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1230_CR12","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1016\/j.jcta.2009.12.009","volume":"117","author":"F Fiedler","year":"2010","unstructured":"Fiedler F., Jedwab J., Wiebe A.: A new source of seed pairs for Golay sequences of length $$2^{m}$$. J. Combin. Theory Ser. A 117, 589\u2013597 (2010).","journal-title":"J. Combin. Theory Ser. A"},{"issue":"7","key":"1230_CR13","doi-asserted-by":"publisher","first-page":"468","DOI":"10.1364\/JOSA.41.000468","volume":"47","author":"MJ Golay","year":"1951","unstructured":"Golay M.J.: static multislit spectrometry and its application to the panoramic display of infrared spectra. J. Opt. Soc. Am. 47(7), 468\u2013472 (1951).","journal-title":"J. Opt. Soc. Am."},{"issue":"7","key":"1230_CR14","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/s10623-007-9088-z","volume":"44","author":"J Jedwab","year":"2007","unstructured":"Jedwab J., Parker M.G.: Golay complementary array pairs. Des. Codes Cryptogr. 44(7), 209\u2013216 (2007).","journal-title":"Des. Codes Cryptogr."},{"key":"1230_CR15","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s10623-007-9060-y","volume":"43","author":"J Jedwab","year":"2007","unstructured":"Jedwab J., Parker M.G.: There are no Barker arrays having more than two dimensions. Des. Codes Cryptogr. 43, 79\u201384 (2007).","journal-title":"Des. Codes Cryptogr."},{"issue":"3","key":"1230_CR16","doi-asserted-by":"publisher","first-page":"1141","DOI":"10.1109\/TIT.2004.842775","volume":"51","author":"Y Li","year":"2005","unstructured":"Li Y., Chu W.B.: More Golay sequences. IEEE Trans. Inf. Theory 51(3), 1141\u20131145 (2005).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1230_CR17","first-page":"70","volume":"21","author":"HD L\u00fcke","year":"1985","unstructured":"L\u00fcke H.D.: Sets of one and higher dimensional Welti codes and complementary codes. Trans. Aerospace Electron. Syst. 21, 70\u2013179 (1985).","journal-title":"Trans. Aerospace Electron. Syst."},{"issue":"1","key":"1230_CR18","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1109\/18.817512","volume":"46","author":"KG Paterson","year":"2000","unstructured":"Paterson K.G.: Generalized Reed-Muller codes and power control in OFDM modulation. IEEE Trans. Inf. Theory 46(1), 104\u2013120 (2000).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1230_CR19","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1016\/0097-3165(74)90056-9","volume":"16","author":"R Turyn","year":"1974","unstructured":"Turyn R.: Hadamard matrices, Baumert-Hall units, four-symbol sequences, pulse compression, and surface wave encodings. J. Combin. Theory Ser. A 16, 313\u2013333 (1974).","journal-title":"J. Combin. Theory Ser. A"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-023-01230-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-023-01230-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-023-01230-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,20]],"date-time":"2023-07-20T20:32:43Z","timestamp":1689885163000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-023-01230-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,6]]},"references-count":19,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["1230"],"URL":"https:\/\/doi.org\/10.1007\/s10623-023-01230-8","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"type":"print","value":"0925-1022"},{"type":"electronic","value":"1573-7586"}],"subject":[],"published":{"date-parts":[[2023,5,6]]},"assertion":[{"value":"5 July 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 December 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 May 2023","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 declare that they have no conflicts of interest relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}